Exhibit 5.1

AI Infrastructure Acquisition Corp.	D +1 345 815 1866
c/o Ogier Global (Cayman) Limited	E natalie.bell@ogier.com
89 Nexus Way, Camana Bay, Grand
Cayman KY1-9009, Cayman Islands	Reference: 513671.00001

	13 August 2025

AI Infrastructure Acquisition Corp. (the Company)

We have been requested to provide you with an opinion on matters of Cayman Islands law in connection with the Company’s registration statement on Form S-1, including all amendments or supplements thereto, filed with the United States Securities and Exchange Commission (the Commission) under the United States Securities Act of 1933 (the Act), as amended, (including its exhibits, the Registration Statement) related to the offering and sale of:

(a)	up to 10,000,000 units (together, the Units), each Unit consisting of one class A ordinary share of the Company with a par value of US$0.0001 each (the Class A Ordinary Shares) and one right to acquire one-fifth of one Class A Ordinary Share (the Rights);

(b)	up to 1,500,000 Units (the Over-Allotment Units) which several underwriters, for whom Maxim Group LLC (Representative) is acting as representative, will have a right to purchase from the Company to cover over-allotments, if any;

(c)	all Class A Ordinary Shares and all Rights issued as part of the Units and the Over-Allotment Units;

(d)	all Class A Ordinary Shares that may be issued upon conversion of the Rights included in the Units and the Over-Allotment Units; and

Ogier (Cayman) LLP

89 Nexus Way

Camana Bay

Grand Cayman, KY1-9009

Cayman Islands

T +1 345 949 9876

F +1 305 513 5888

ogier.com

AI Infrastructure Acquisition Corp.

13 August 2025

(e)	up to 402,500 Class A Ordinary Shares to the Representative (Representative Shares).

This opinion is given in accordance with the terms of the Legal Matters section of the Registration Statement.

Unless a contrary intention appears, all capitalised terms used in this opinion have the respective meanings set forth in Schedule 1. A reference to a Schedule is a reference to a schedule to this opinion and the headings herein are for convenience only and do not affect the construction of this opinion.

1	Documents examined

For the purposes of giving this opinion, we have examined the corporate and other documents and conducted the searches listed in Schedule 1. We have not made any searches or enquiries concerning, and have not examined any documents entered into by or affecting the Company or any other person, save for the searches, enquiries and examinations expressly referred to in Schedule 1.

2	Assumptions

In giving this opinion we have relied upon the assumptions set forth in Schedule 18 without having carried out any independent investigation or verification in respect of those assumptions.

3	Opinions

On the basis of the examinations and assumptions referred to above and subject to the qualifications set forth in Schedule 3 and the limitations set forth below, we are of the opinion that:

Corporate status

(a)

The Company has been duly incorporated as an exempted company with limited liability and is validly existing and in good standing with the Registrar of Companies of the Cayman Islands (the Registrar).

Corporate power

(b)

The Company will have under the A&R M&A all requisite power to issue the Class A Ordinary Shares (including the issuance of the Class A Ordinary Shares upon the conversion of the Rights in accordance with the Rights Documents and the Representative Shares), to execute and deliver the Documents and to perform its obligations, and conversion its rights, under such documents.

AI Infrastructure Acquisition Corp.

13 August 2025

Corporate authorisation

(c)

The Company has taken all requisite corporate action to authorise:

(i)

the issuance of the Class A Ordinary Shares (including the issuance of the Class A Ordinary Shares upon the conversion of the Rights in accordance with the Rights Documents and the Representative Shares); and

(ii)

the execution and delivery of the Documents and the performance of its obligations, and the exercise of its rights, under such documents.

Shares

(d)

The Class A Ordinary Shares to be offered and issued by the Company as contemplated by the Registration Statement (including the issuance of the Class A Ordinary Shares upon the conversion of the Rights in accordance with the Rights Documents and the Representative Shares), when issued by the Company upon:

(i)

payment in full of the consideration as set out in the Registration Statement and in accordance with the terms set out in the Registration Statement (including the issuance of the Class A Ordinary Shares upon the conversion of the Rights in accordance with the Rights Documents and the Representative Shares) and in accordance with the A&R M&A; and

(ii)

the entry of those Class A Ordinary Shares as fully paid on the register of members of the Company,

shall be validly issued, fully paid and non-assessable.

4	Matters not covered

We offer no opinion:

(a)

as to any laws other than the laws of the Cayman Islands, and we have not, for the purposes of this opinion, made any investigation of the laws of any other jurisdiction, and we express no opinion as to the meaning, validity, or effect of references in the Documents to statutes, rules, regulations, codes or judicial authority of any jurisdiction other than the Cayman Islands;

(b)

except to the extent that this opinion expressly provides otherwise, as to the commercial terms of, or the validity, enforceability or effect of the documents reviewed (or as to how the commercial terms of such documents reflect the intentions of the parties), the accuracy of representations, the fulfilment of warranties or conditions, the occurrence of events of default or terminating events or the existence of any conflicts or inconsistencies among the documents and any other agreements into which the Company may have entered or any other documents; or

AI Infrastructure Acquisition Corp.

13 August 2025

(c)

as to whether the acceptance, execution or performance of the Company’s obligations under the documents reviewed by us will result in the breach of or infringe any other agreement, deed or document (other than, to the extent expressly provided herein, the Company’s Memorandum and Articles of Association or the A&R M&A) entered into by or binding on the Company.

5	Governing law of this opinion

5.1	This opinion is:

(a)

governed by, and shall be construed in accordance with, the laws of the Cayman Islands;

(b)

limited to the matters expressly stated in it; and

(c)

confined to, and given on the basis of, the laws and practice in the Cayman Islands at the date of this opinion.

5.2	Unless otherwise indicated, a reference to any specific Cayman Islands legislation is a reference to that legislation as amended to, and as in force at, the date of this opinion.

6	Consent

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and also consent to the reference to this firm in the Registration Statement under the heading “Legal Matters”. In the giving of our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the Rules and Regulations of the Commission thereunder.

Yours faithfully

Ogier (Cayman) LLP

AI Infrastructure Acquisition Corp.

13 August 2025

Schedule 1

Documents examined

Corporate and other documents

1	The Certificate of Incorporation of the Company dated 13 May 2025 issued by the Registrar.

2	The memorandum and articles of association of the Company dated 13 May 2025 (the Memorandum and Articles of Association).

3	The draft amended and restated memorandum and articles of association of the Company appended to the Registration Statement (the A&R M&A).

4	A Certificate of Good Standing dated 13 August 2025 (the Good Standing Certificate) issued by the Registrar in respect of the Company.

A certificate dated on the date hereof as to certain matters of fact signed by a director of the Company in the form annexed hereto (the Director’s Certificate), having attached to it a copy of the minutes of the meeting of the board of directors of the Company held on 30 May 2025 and the written resolutions of all of the directors of the board of the directors of the Company dated 8 August 2025 (the Resolutions).

6	The Register of Writs at the office of the Clerk of Courts in the Cayman Islands as inspected by us on 13 August 2025 (the Register of Writs).

7	The Registration Statement.

8	A draft of the form of the unit certificate representing the Units and the Over-Allotment Units (the Unit Certificates).

9	A draft specimen certificate for Class A Ordinary Shares (the Share Certificates).

10	A draft of the form of the rights agreement and the rights certificate constituting the Rights (the Rights Documents and, together with the Unit Certificates and the Share Certificates, the Documents).

AI Infrastructure Acquisition Corp.

13 August 2025

Schedule 2

Assumptions

Assumptions of general application

1	All original documents examined by us are authentic and complete.

2	All copy documents examined by us (whether in facsimile, electronic or other form) conform to the originals and those originals are authentic and complete.

3	All signatures, seals, dates, stamps and markings (whether on original or copy documents) are genuine.

4	Each of the Good Standing Certificate and the Director’s Certificate is accurate and complete as at the date of this opinion.

Where any Document has been provided to us in draft or undated form, that Document has been executed by all parties in materially the form provided to us and, where we have been provided with successive drafts of a Document marked to show changes from a previous draft, all such changes have been accurately marked.

6	There will be no intervening circumstance relevant to this opinion between the date hereof and the date upon which the Class A Ordinary Shares are issued.

7	There is nothing in any law (other than the laws of the Cayman Islands) that would or might affect the opinions herein.

Status, authorisation and execution

8	Each of the parties to the Documents other than the Company is duly incorporated, formed or organised (as applicable), validly existing and in good standing under all relevant laws.

In authorising the execution and delivery of the Documents by the Company, the issue and allotment of the Class A Ordinary Shares and the Rights, and the exercise of its rights and performance of its obligations under the Documents, each of the directors of the Company has acted in good faith with a view to the best interests of the Company and has exercised the standard of care, diligence and skill that is required of him or her.

AI Infrastructure Acquisition Corp.

13 August 2025

Enforceability

10	None of the opinions expressed herein will be adversely affected by the laws or public policies of any jurisdiction other than the Cayman Islands. In particular, but without limitation to the previous sentence:

(a)

the laws or public policies of any jurisdiction other than the Cayman Islands will not adversely affect the capacity or authority of the Company; and

(b)

neither the execution or delivery of the Documents nor the exercise by any party to the Documents of its rights or the performance of its obligations under them contravene those laws or public policies.

Share Issuance

11	The Class A Ordinary Shares to be issued shall be issued at an issue price in excess of the par value thereof.

12	The draft A&R M&A will be adopted by the Company in accordance with the Memorandum and Articles of Association prior to the date that any Units, Class A Ordinary Shares, Rights, or Over-Allotment Units are issued by the Company.

Register of Writs

13	The Register of Writs constitutes a complete and accurate record of the proceedings affecting the Company before the Grand Court of the Cayman Islands as at the time we conducted our investigation of such register.

AI Infrastructure Acquisition Corp.

13 August 2025

Schedule 3

Qualifications

Good Standing

Under the Companies Act (Revised) of the Cayman Islands (Companies Act) annual returns in respect of the Company must be filed with the Registrar, together with payment of annual filing fees. A failure to file annual returns and pay annual filing fees may result in the Company being struck off the Register of Companies, following which its assets will vest in the Financial Secretary of the Cayman Islands and will be subject to disposition or retention for the benefit of the public of the Cayman Islands.

In good standing means only that as of the date of the Good Standing Certificate the Company is up-to-date with the filing of its annual returns and payment of annual fees with the Registrar. We have made no enquiries into the Company’s good standing with respect to any filings or payment of fees, or both, that it may be required to make under the laws of the Cayman Islands other than the Companies Act.

Limited Liability

We are not aware of any Cayman Islands authority as to when the courts would set aside the limited liability of a shareholder in a Cayman Islands company. Our opinion on the subject is based on the Companies Act and English common law authorities, the latter of which are persuasive but not binding in the courts of the Cayman Islands. Under English authorities, circumstances in which a court would attribute personal liability to a shareholder are very limited, and include: (a) such shareholder expressly assuming direct liability (such as a guarantee); (b) the company acting as the agent of such shareholder; and (c) the company being incorporated by or at the behest of such shareholder for the purpose of committing or furthering such shareholder’s fraud, or for a sham transaction otherwise carried out by such shareholder. In the absence of these circumstances, we are of the opinion that a Cayman Islands’ court would have no grounds to set aside the limited liability of a shareholder.

Non-Assessable

In this opinion, the phrase “non-assessable” means, with respect to the Class A Ordinary Shares in the Company, that a shareholder shall not, solely by virtue of its status as a shareholder, be liable for additional assessments or calls on the Class A Ordinary Shares by the Company or its creditors (except in exceptional circumstances, such as involving fraud, the establishment of an agency relationship or an illegal or improper purpose or other circumstance in which a court may be prepared to pierce or lift the corporate veil).

5	Our examination of the Register of Writs cannot conclusively reveal whether or not there is:

(a)

any current or pending litigation in the Cayman Islands against the Company; or

(b)

any application for the winding up or dissolution of the Company or the appointment of any liquidator, trustee in bankruptcy or restructuring officer in respect of the Company or any of its assets,

as notice of these matters might not be entered on the Register of Writs immediately or updated expeditiously or the court file associated with the matter or the matter itself may not be publicly available (for example, due to sealing orders having been made). Furthermore, we have not conducted a search of the summary court. Claims in the summary court are limited to a maximum of CI $20,000.

AI Infrastructure Acquisition Corp. S-1