Exhibit 5.1

345 Park Avenue
New York, NY 10154

Main 212.407.4000
Fax 212.407.4990
mnussbaum@loeb.com

June 1, 2026

BlockchAIn Digital Infrastructure, Inc.
1540 Broadway, Suite 1010
New York, New York 10036

Re:	BlockchAIn Digital Infrastructure, Inc. - Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to BlockchAIn Digital Infrastructure, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of the Company’s registration statement on Form S-1 (as amended or supplemented from time to time, the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), filed by the Company with the Securities and Exchange Commission (the “Commission”), including the prospectus contained therein (the “Prospectus”). The Registration Statement relates to the offering by the Company of up to a maximum aggregate offering price of $72,036,000of (i) shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), (ii) pre-funded warrants (the “Pre-funded Warrants”) to purchase shares of Common Stock (the “Pre-funded Warrant Shares”), (iii) the Pre-funded Warrant Shares underlying the Pre-Funded Warrants, (iv) additional shares of Common Stock (the “Option Shares”) that may be purchased by the representative of the underwriters pursuant to an option granted by the Company to cover over-allotments, if any (the “Over-allotment Option”), (v) warrants to be issued to the representative of the underwriters in the Company’s offering (the “Representative Warrants”) to purchase up to 4% of the number of shares of Common Stock sold in the offering, including any shares of Common Stock sold to cover over-allotments, if any, and (vi) the shares of Common Stock underlying the Representative Warrants (the “Representative Shares”). The Shares, the Pre-funded Warrants, the Option Shares and the Representative Warrants will be sold by the Company pursuant to an underwriting agreement to be entered into by and between the Company and Lucid Capital Partners, LLC, acting as representative of the several underwriters named therein, in the form filed as Exhibit 1.1 to the Registration Statement (the “Underwriting Agreement”).

In connection with this opinion letter, we have examined and relied upon original, certified, conformed, photostat or other copies of (a) the Amended and Restated Certificate of Incorporation, and the Amended and Restated Bylaws, of the Company, (b) resolutions of the board of directors of the Company, (c) the Registration Statement and the exhibits thereto; (d) the form of Underwriting Agreement, (e) the form of Pre-funded Warrant, (f) the form of Representative Warrant, and (g) such corporate records of the Company, certificates of public officials, certificates of officers of the Company and other documents, agreements and instruments as we have deemed necessary as a basis for the opinions herein contained. In all such examinations, we have assumed the genuineness of all signatures on original documents, and the conformity to originals or certified documents of all copies submitted to us as conformed, photostat or other copies. In passing upon certain corporate records and documents of the Company, we have assumed the correctness and completeness of the statements made or included therein by the Company, and we express no opinion thereon.

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We have further assumed the legal capacity of natural persons, and we have assumed that each party to the documents we have examined or relied on (other than the Company) has the legal capacity or authority and has satisfied all legal requirements that are applicable to that party to the extent necessary to make such documents enforceable against that party.

Based upon the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that:

The Shares have been duly authorized for issuance by the Company and, when issued, delivered and paid for in accordance with the terms of the Underwriting Agreement, the Registration Statement and the Prospectus, the Shares will be validly issued, fully paid and non-assessable.

The Pre-funded Warrants have been duly authorized for issuance by the Company and, when issued, delivered and paid for in accordance with the terms of the Underwriting Agreement, the Registration Statement and the Prospectus the Pre-funded Warrants will be valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

The Pre-funded Warrant Shares have been duly authorized for issuance by the Company and, when issued and delivered upon the exercise of the Pre-funded Warrants in accordance with the terms of the Pre-funded Warrants, including without limitation, the payment in full of applicable consideration, the Pre-funded Warrant Shares will be validly issued, fully paid and non-assessable.

The Option Shares have been duly authorized for issuance by the Company and, when issued and delivered and paid for upon the exercise of the Over-allotment Option in accordance with the terms of the Underwriting Agreement, the Registration Statement and the Prospectus, the Option Shares will be validly issued, fully paid and non-assessable.

The Representative Warrants have been duly authorized for issuance by the Company and, when issued and delivered by the Company in accordance with the terms of the Underwriting Agreement, the Registration Statement and the Prospectus, the Representative Warrants will be valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

The Representative Shares have been duly authorized for issuance by the Company and, when issued and delivered upon the exercise of the Representative’s Warrants in accordance with the terms of the Representative Warrants, including, without limitation, the payment in full of applicable consideration, the Representative Shares will be validly issued, fully paid and non-assessable.

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The opinions we express above are based upon a review only of those laws, statutes, rules, ordinances and regulations which, in our experience, a securities lawyer who is a member of the bar of the State of New York and practicing before the Commission exercising customary professional diligence would reasonably recognize as being applicable to the foregoing transactions.

The opinions set forth in paragraphs 2 and 5 above are subject to (i) the effect of any applicable bankruptcy, insolvency, reorganization, moratorium or similar law relating to or affecting creditors’ rights generally (including, without limitation, fraudulent conveyance laws) and (ii) the effect of general principles of equity, including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief, regardless of whether considered in a proceeding in equity or at law.

We express no opinion as to the enforceability of (i) provisions that relate to choice of law, forum selection or submission to jurisdiction (including, without limitation, any express or implied waiver of any objection to venue in any court or of any objection that a court is an inconvenient forum) to the extent that the validity, binding effect or enforceability of any such provision is to be determined by any court other than a state court of the State of New York and (ii) waivers by the Company of any statutory or constitutional rights or remedies. We draw your attention to the fact that, under certain circumstances, the enforceability of terms to the effect that provisions may not be waived or modified except in writing may be limited.

The opinions we express herein are limited to matters involving the internal laws of the State of New York and the Delaware General Corporation law.

We hereby consent to the filing of this opinion letter with the Commission as Exhibit 5.1 to the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S−K under the Securities Act and to the reference to our firm therein and in the Prospectus under the caption “Legal Matters.” In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act, or the rules and regulations promulgated thereunder.

Very truly yours,

/s/ Loeb & Loeb LLP

Loeb & Loeb LLP