Exhibit 10.5

VINE HILL CAPITAL INVESTMENT CORP. II

500 E Broward Blvd., Suite 900

Fort Lauderdale, FL 33394

August 21, 2025

Vine Hill Capital Sponsor II LLC

500 E Broward Blvd., Suite 900

Fort Lauderdale, FL 33394

Ladies and Gentlemen:

Vine Hill Capital Investment Corp. II, a Cayman Islands exempted company (the “Company”), is pleased to accept the offer Vine Hill Capital Sponsor II LLC, a Delaware limited liability company (the “Subscriber”), has made to purchase 6,708,333 Class B ordinary shares of the Company (the “Founder Shares”), $0.0001 par value per share (the “Class B Ordinary Shares”), up to 875,000 of which are subject to complete or partial forfeiture by the Subscriber if the underwriters of the proposed initial public offering (“IPO”) of the Company pursuant to the registration statement on Form S-1 expected to be filed by the Company in connection with the IPO (the “Registration Statement”) do not fully exercise their over-allotment option (the “Over-allotment Option”). For the purposes of this Agreement, references to “Ordinary Shares” are to, collectively, the Class B Ordinary Shares and the Company’s Class A ordinary shares, $0.0001 par value per share (the “Class A Ordinary Shares”). Pursuant to the Company’s memorandum and articles of association in effect as of the date hereof (the “Charter”), Class B Ordinary Shares will automatically convert into Class A Ordinary Shares on a one-for-one basis, subject to adjustment, upon the terms and conditions set forth in the Charter. Unless the context otherwise requires, as used herein “Securities” shall refer to the Founder Shares and shall be deemed to include any Class A Ordinary Shares issued or deemed issued upon conversion of the Founder Shares. The terms (this “Agreement”) on which the Company is willing to sell the Founder Shares to the Subscriber, and the Company and the Subscriber’s agreements regarding such Founder Shares, are as follows:

1. Purchase of Founder Shares and Surrender of Subscriber Share.

1.1 Purchase of Founder Shares. For the sum of $25,000 (the “Purchase Price”), which the Company acknowledges receiving in cash, the Company hereby sells, issues and allots the Founder Shares to the Subscriber, and the Subscriber hereby purchases the Founder Shares from the Company, subject to the forfeiture provisions of Section 3 below, on the terms and subject to the conditions set forth in this Agreement. Concurrently with the Subscriber’s execution of this Agreement, the Company shall, at its option, deliver to the Subscriber a certificate registered in the Subscriber’s name representing the Founder Shares (the “Original Certificate”), or effect such delivery in book-entry form.

1.2 Surrender of Subscriber Share. The Subscriber hereby irrevocably surrenders to the Company for cancellation and for nil consideration 1 Class B Ordinary Share standing in its name in the register of members of the Company in accordance with Section 37B of the Companies Act (As Revised) of the Cayman Islands.

2. Representations, Warranties and Agreements.

2.1 Subscriber’s Representations, Warranties and Agreements. To induce the Company to issue the Securities to the Subscriber, the Subscriber hereby represents and warrants to the Company and agrees with the Company as follows:

2.1.1 No Government Recommendation or Approval. The Subscriber understands that no federal or state agency has passed upon or made any recommendation or endorsement of the offering of the Securities.

2.1.2 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Subscriber of the transactions contemplated hereby do not violate, conflict with or constitute a default under (i) the formation and governing documents of the Subscriber, (ii) any agreement, indenture or instrument to which the Subscriber is a party, (iii) any law, statute, rule or regulation to which the Subscriber is subject, or (iv) any agreement, order, judgment or decree to which the Subscriber is subject.

2.1.3 Organization and Authority. The Subscriber is a Delaware limited liability company, validly existing and in good standing under the laws of Delaware and possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement. Upon execution and delivery by you, this Agreement will be a legal, valid and binding agreement of the Subscriber, enforceable against the Subscriber in accordance with its terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance or similar laws affecting the enforcement of creditors’ rights generally and subject to general principles of equity (regardless of whether enforcement is sought in a proceeding at law or in equity).

2.1.4 Experience, Financial Capability and Suitability. The Subscriber is: (i) sophisticated in financial matters and is able to evaluate the risks and benefits of the investment in the Securities and (ii) able to bear the economic risk of its investment in the Securities for an indefinite period of time because the Securities have not been registered under the Securities Act (as defined below) and therefore cannot be sold unless subsequently registered under the Securities Act or an exemption from such registration is available. The Subscriber is capable of evaluating the merits and risks of its investment in the Company and has the capacity to protect its own interests. The Subscriber must bear the economic risk of this investment until the Securities are sold pursuant to: (i) an effective registration statement under the Securities Act or (ii) an exemption from registration available with respect to such sale. The Subscriber is able to bear the economic risks of an investment in the Securities and to afford a complete loss of the Subscriber’s investment in the Securities.

2.1.5 Access to Information; Independent Investigation. Prior to the execution of this Agreement, the Subscriber has had the opportunity to ask questions of and receive answers from representatives of the Company concerning an investment in the Company, as well as the finances, operations, business and prospects of the Company, and the opportunity to obtain additional information to verify the accuracy of all information so obtained. In determining whether to make this investment, the Subscriber has relied solely on the Subscriber’s own knowledge and understanding of the Company and its business based upon the Subscriber’s own due diligence investigation and the information furnished pursuant to this paragraph. The Subscriber understands that no person has been authorized to give any information or to make any representations which were not furnished pursuant to this Section 2 and the Subscriber has not relied on any other representations or information in making its investment decision, whether written or oral, relating to the Company, its operations or its prospects.

2.1.6 Regulation D Offering. The Subscriber represents that it is an “accredited investor” as such term is defined in Rule 501(a) of Regulation D under the Securities Act of 1933, as amended (the “Securities Act”), and acknowledges the sale contemplated hereby is being made in reliance on a private placement exemption applicable to “accredited investors” within the meaning of Section 501(a) of Regulation D under the Securities Act or similar exemptions under federal and state law.

2.1.7 Investment Purposes. The Subscriber is purchasing the Securities solely for investment purposes, for the Subscriber’s own account and not for the account or benefit of any other person, and not with a view towards the distribution or dissemination thereof. The Subscriber did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning of Rule 502 of Regulation D under the Securities Act.

2.1.8 Restrictions on Transfer; Shell Company. The Subscriber understands the Securities are being offered in a transaction not involving a public offering within the meaning of the Securities Act. The Subscriber understands the Securities will be “restricted securities” within the meaning of Rule 144(a)(3) under the Securities Act and the Subscriber understands that the certificates or book-entries representing the Securities will contain a legend in respect of such restrictions. If in the future the Subscriber decides to offer, resell, pledge or otherwise transfer the Securities, such Securities may be offered, resold, pledged or otherwise transferred only pursuant to: (i) registration under the Securities Act, or (ii) an available exemption from registration. The Subscriber agrees that if any transfer of its Securities or any interest therein is proposed to be made, as a condition precedent to any such transfer, the Subscriber may be required to deliver to the Company an opinion of counsel satisfactory to the Company. Absent registration under the Securities Act or an exemption therefrom, the Subscriber agrees not to resell the Securities. The Subscriber further acknowledges that because the Company is a shell company, Rule 144 may not be available to the Subscriber for the resale of the Founder Shares until at least one year following consummation of the initial business combination of the Company, despite technical compliance with the requirements of Rule 144 and the release or waiver of any contractual transfer restrictions.

2.1.9 No Governmental Consents. No governmental, administrative or other third party consents or approvals are required, necessary or appropriate on the part of the Subscriber in connection with the transactions contemplated by this Agreement.

2.2 Company’s Representations, Warranties and Agreements. To induce the Subscriber to purchase the Securities, the Company hereby represents and warrants to the Subscriber and agrees with the Subscriber as follows:

2.2.1 Organization and Corporate Power. The Company is a Cayman Islands exempted company and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the Company. The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement.

2.2.2 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Company of the transactions contemplated hereby do not violate, conflict with or constitute a default under (i) the Charter, (ii) any agreement, indenture or instrument to which the Company is a party or (iii) any law, statute, rule or regulation to which the Company is subject, or any agreement, order, judgment or decree to which the Company is subject.

2.2.3 Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof, and upon registration in the register of members of the Company, the Securities will be duly and validly issued, fully paid and nonassessable. Upon issuance in accordance with, and payment pursuant to, the terms hereof, and upon registration in the register of members of the Company, the Subscriber will have or receive good title to the Securities, free and clear of all liens, claims and encumbrances of any kind, other than (a) transfer restrictions hereunder and under the other agreements to which the Securities may be subject, (b) transfer restrictions under federal and state securities laws, and (c) liens, claims or encumbrances imposed due to the actions of the Subscriber.

2.2.4 No Adverse Actions. There are no actions, suits, investigations or proceedings pending, threatened against or affecting the Company which: (i) seek to restrain, enjoin, prevent the consummation of or otherwise affect the transactions contemplated by this Agreement or (ii) question the validity or legality of any transactions or seek to recover damages or to obtain other relief in connection with any transactions.

2.2.5 Authorization. The Class A Ordinary Shares issuable upon conversion of the Founder Shares have been duly authorized and reserved for issuance upon such conversion.

3. Forfeiture of Founder Shares.

3.1 Partial or No Exercise of the Over-allotment Option. In the event the Over-allotment Option granted to the underwriters of the IPO is not exercised in full, the Subscriber acknowledges and agrees that it (or, if applicable, it and any transferees of Founder Shares) shall automatically forfeit and surrender for no consideration at the time such Over-allotment Option expires (or earlier if the underwriters of the IPO waive their ability to exercise such Over-allotment Option) any and all rights to such number of Founder Shares (up to an aggregate of 875,000 Founder Shares and pro rata based upon the percentage of the Over-allotment Option exercised) such that immediately following such forfeiture, the Subscriber (and any such transferees), collectively with all other initial shareholders of the Company prior to the IPO, if any, will own an aggregate number of Founder Shares equal to 25% of the issued and outstanding Ordinary Shares immediately following the IPO.

3.2 Termination of Rights as Shareholder. If any of the Founder Shares are forfeited and surrendered in accordance with this Section 3, then after such time the Subscriber (or its successor in interest), shall no longer have any rights as a holder of such forfeited and surrendered Founder Shares, and the Company shall take such action as is appropriate to cancel such forfeited and surrendered Founder Shares in the register of members of the Company.

3.3 Share Certificates. In the event an adjustment to the Original Certificates, if any, is required pursuant to this Section 3, then the Subscriber shall return such Original Certificates to the Company or its designated agent as soon as practicable upon its receipt of notice from the Company advising the Subscriber of such adjustment, following which a new certificate (the “New Certificate”), if any, shall be issued in such amount representing the adjusted number of Founder Shares held by the Subscriber. The New Certificate, if any, shall be returned to the Subscriber as soon as practicable. Any such adjustment for any uncertificated securities held by the Subscriber shall be made in book-entry form.

4. Waiver of Liquidation Distributions; Redemption Rights. In connection with the Founder Shares purchased pursuant to this Agreement, the Subscriber hereby waives any and all right, title, interest or claim of any kind in or to any distributions by the Company from the trust account which will be established for the benefit of the Company’s public shareholders and into which substantially all of the proceeds of the IPO will be deposited (the “Trust Account”), in the event of a liquidation of the Company upon the Company’s failure to timely complete an initial business combination. For purposes of clarity, in the event the Subscriber purchases securities in the IPO or securities of the Company issued in the IPO in the aftermarket, any additional Ordinary Shares so purchased shall be eligible to receive any liquidating distributions from the Trust Account by the Company. However, in no event will the Subscriber have the right to redeem any Ordinary Shares into funds held in the Trust Account upon the successful completion of an initial business combination.

5. Restrictions on Transfer.

5.1 Securities Law Restrictions. In addition to any restrictions to be contained in that certain letter agreement (commonly known as an “Insider Letter”) to be entered into between the Subscriber and the Company (which will also contain other agreements with respect to the Securities) in connection with the consummation of the IPO, the Subscriber agrees not to sell, transfer, pledge, hypothecate or otherwise dispose of all or any part of the Securities unless, prior thereto (a) a registration statement on the appropriate form under the Securities Act and applicable state securities laws with respect to the Securities proposed to be transferred shall then be effective or (b) the Company has received an opinion from counsel reasonably satisfactory to the Company, that such registration is not required because such transaction is exempt from registration under the Securities Act and the rules promulgated by the Securities and Exchange Commission thereunder and with all applicable state securities laws.

5.2 Restrictive Legends. All certificates representing the Securities shall have endorsed thereon legends substantially as follows:

“THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS AND NEITHER THE SECURITIES NOR ANY INTEREST THEREIN MAY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT OR SUCH LAWS OR AN EXEMPTION FROM REGISTRATION UNDER SUCH ACT AND SUCH LAWS WHICH, IN THE OPINION OF COUNSEL (IF THE COMPANY SO REQUESTS), IS AVAILABLE.”

“THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO LOCKUP PROVISIONS AND MAY NOT BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED DURING THE TERM OF THE LOCKUP PERIOD.”

5.3 Additional Founder Shares or Substituted Securities. In the event of the declaration of a share dividend, the declaration of an extraordinary dividend payable in a form other than Ordinary Shares, a spin-off, a share sub-division, an adjustment in conversion ratio, a recapitalization or a similar transaction affecting the Company’s outstanding Ordinary Shares without receipt of consideration, any new, substituted or additional securities or other property which are by reason of such transaction distributed with respect to any Securities subject to this Section 5 or into which such Securities thereby become convertible shall immediately be subject to this Section 5 and Section 3. Appropriate adjustments to reflect the distribution of such securities or property shall be made to the number and/or class of Securities subject to this Section 5 and Section 3.

6. Other Agreements.

6.1 Further Assurances. The Subscriber agrees to execute such further instruments and to take such further action as may reasonably be necessary to carry out the intent of this Agreement.

6.2 Notices. All notices, statements or other documents which are required or contemplated by this Agreement shall be in writing and delivered (i) personally or sent by first class registered or certified mail, overnight courier service or facsimile or electronic transmission to the address designated in writing, (ii) by facsimile to the number most recently provided to such party or such other address or fax number as may be designated in writing by such party, and (iii) by electronic mail, to the electronic mail address most recently provided to such party or such other electronic mail address as may be designated in writing by such party. Any notice or other communication so transmitted shall be deemed to have been given on the day of delivery, if delivered personally, on the business day following receipt of written confirmation, if sent by facsimile or electronic transmission, one (1) business day after delivery to an overnight courier service or five (5) days after mailing if sent by mail.

6.3 Entire Agreement. This Agreement, together with that certain Insider Letter to be entered into between the Subscriber and the Company and the registration rights agreement to be entered into with respect to the Securities, each substantially in the form to be filed as an exhibit to the Registration Statement, embodies the entire agreement and understanding between the Subscriber and the Company with respect to the subject matter hereof and supersedes all prior oral or written agreements and understandings relating to the subject matter hereof. No statement, representation, warranty, covenant or agreement of any kind not expressly set forth in this Agreement shall affect, or be used to interpret, change or restrict, the express terms and provisions of this Agreement.

6.4 Modifications and Amendments. The terms and provisions of this Agreement may be modified or amended only by written agreement executed by all parties hereto.

6.5 Waivers and Consents. The terms and provisions of this Agreement may be waived, or consent for the departure therefrom granted, only by written document executed by the party entitled to the benefits of such terms or provisions. No such waiver or consent shall be deemed to be or shall constitute a waiver or consent with respect to any other terms or provisions of this Agreement, whether or not similar. Each such waiver or consent shall be effective only in the specific instance and for the purpose for which it was given, and shall not constitute a continuing waiver or consent.

6.6 Assignment. The rights and obligations under this Agreement may not be assigned by either party hereto without the prior written consent of the other party.

6.7 Benefit. All statements, representations, warranties, covenants and agreements in this Agreement shall be binding on the parties hereto and shall inure to the benefit of the respective successors and permitted assigns of each party hereto. Nothing in this Agreement shall be construed to create any rights or obligations except among the parties hereto, and no person or entity shall be regarded as a third-party beneficiary of this Agreement.

6.8 Governing Law. This Agreement and the rights and obligations of the parties hereunder shall be construed in accordance with and governed by the laws of the State of New York applicable to contracts wholly performed within the borders of such state.

6.9 Severability. In the event that any court of competent jurisdiction shall determine that any provision, or any portion thereof, contained in this Agreement shall be unreasonable or unenforceable in any respect, then such provision shall be deemed limited to the extent that such court deems it reasonable and enforceable, and as so limited shall remain in full force and effect. In the event that such court shall deem any such provision, or portion thereof, wholly unenforceable, the remaining provisions of this Agreement shall nevertheless remain in full force and effect.

6.10 No Waiver of Rights, Powers and Remedies. No failure or delay by a party hereto in exercising any right, power or remedy under this Agreement, and no course of dealing between the parties hereto, shall operate as a waiver of any such right, power or remedy of such party. No single or partial exercise of any right, power or remedy under this Agreement by a party hereto, nor any abandonment or discontinuance of steps to enforce any such right, power or remedy, shall preclude such party from any other or further exercise thereof or the exercise of any other right, power or remedy hereunder. The election of any remedy by a party hereto shall not constitute a waiver of the right of such party to pursue other available remedies. No notice to or demand on a party not expressly required under this Agreement shall entitle the party receiving such notice or demand to any other or further notice or demand in similar or other circumstances or constitute a waiver of the rights of the party giving such notice or demand to any other or further action in any circumstances without such notice or demand.

6.11 Survival of Representations and Warranties. All representations and warranties made by the parties hereto in this Agreement or in any other agreement, certificate or instrument provided for or contemplated hereby, shall survive the execution and delivery hereof and any investigations made by or on behalf of the parties.

6.12 No Broker or Finder. Each of the parties hereto represents and warrants to the other that no broker, finder or other financial consultant has acted on its behalf in connection with this Agreement or the transactions contemplated hereby in such a way as to create any liability on the other. Each of the parties hereto agrees to indemnify and hold the other harmless from any claim or demand for commission or other compensation by any broker, finder, financial consultant or similar agent claiming to have been employed by or on behalf of such party and to bear the cost of legal expenses incurred in defending against any such claim.

6.13 Headings and Captions. The headings and captions of the various sections of this Agreement are for convenience of reference only and shall in no way modify or affect the meaning or construction of any of the terms or provisions hereof.

6.14 Counterparts. This Agreement may be executed in one or more counterparts, all of which when taken together shall be considered one and the same agreement and shall become effective when counterparts have been signed by each party and delivered to the other party, it being understood that both parties need not sign the same counterpart. In the event that any signature is delivered by facsimile transmission or any other form of electronic delivery, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such signature page were an original thereof. This Agreement may be delivered via facsimile, electronic mail (including any electronic signature covered by the U.S. federal ESIGN Act of 2000, Uniform Electronic Transactions Act, the Electronic Signatures and Records Act or other applicable law (e.g., www.docusign.com)) or other transmission method and any counterpart so delivered shall be deemed to have been duly and validly delivered and be valid and effective for all purposes.

6.15 Construction. The parties hereto have participated jointly in the negotiation and drafting of this Agreement. If an ambiguity or question of intent or interpretation arises, this Agreement will be construed as if drafted jointly by the parties hereto and no presumption or burden of proof will arise favoring or disfavoring any party hereto because of the authorship of any provision of this Agreement. The words “include,” “includes,” and “including” will be deemed to be followed by “without limitation.” Pronouns in masculine, feminine, and neuter genders will be construed to include any other gender, and words in the singular form will be construed to include the plural and vice versa, unless the context otherwise requires. The words “this Agreement,” “herein,” “hereof,” “hereby,” “hereunder,” and words of similar import refer to this Agreement as a whole and not to any particular section unless expressly so limited. The parties hereto intend that each representation, warranty, and covenant contained herein will have independent significance. If any party hereto has breached any representation, warranty, or covenant contained herein in any respect, the fact that there exists another representation, warranty or covenant relating to the same subject matter (regardless of the relative levels of specificity) which such party hereto has not breached will not detract from or mitigate the fact that such party hereto is in breach of the first representation, warranty, or covenant.

6.16 Mutual Drafting. This Agreement is the joint product of the Subscriber and the Company and each provision hereof has been subject to the mutual consultation, negotiation and agreement of such parties and shall not be construed for or against any party hereto.

7. Indemnification. Each party shall indemnify the other against any loss, cost or damages (including reasonable attorney’s fees and expenses) incurred as a result of such party’s breach of any representation, warranty, covenant or agreement in this Agreement.

[Signature Page Follows]

If the foregoing accurately sets forth our understanding and agreement, please sign the enclosed copy of this Agreement and return it to us.

	Very truly yours,

	VINE HILL CAPITAL INVESTMENT CORP. II

	By:	/s/ Nicholas Petruska
	Name:	Nicholas Petruska
	Title:	Director

VINE HILL CAPITAL SPONSOR II LLC

By:	/s/ Nicholas Petruska
Name:	Nicholas Petruska
Title:	Managing Member

Vine Hill Capital Investment Corp. II S-1/A