Exhibit 5.1

September 8, 2026

CDT Equity Inc.

4851 Tamiami Trail North, Suite 200

Naples, FL 34103

Ladies and Gentlemen:

We have acted as counsel for CDT Equity Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of a Registration Statement on Form S-1 (the “Registration Statement”), with the U.S. Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), with respect to the resale, on a delayed or continuous basis, by the selling stockholders named in the Registration Statement under the caption “Selling Stockholders” (the “Selling Stockholders”) of up to an aggregate of 16,825,644 shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), consisting of (i) 365,750 shares of Common Stock (the “Warrant Shares”) underlying common stock purchase warrants (the “Warrants”) issued to J.J. Astor & Co. (the “Lender”) (ii) 3,523,125 shares of Common Stock (the “Conversion Shares”) issuable pursuant to the senior secured convertible promissory note, dated June 11, 2026, as amended and restated on July 31, 2026 and August 3, 2026, in $2,536,650 aggregate principal amount and an additional $541,620 senior secured convertible promissory notes issued to the Lender on August 31, 2026 (collectively, the “Notes”), (iii) 32,110 shares of Common Stock issued to EX-ANIMO Ltd. on July 24, 2026 for consulting services, (iv) 25,000 shares of Common Stock issued to Maxim Partners LLC on July 30, 2026 as consideration for services provided to the Company, (v) 31,373 shares of Common Stock issued to Ian Burton on July 30, 2026 as consideration for services provided to the Company, (vi) 12,131,122 shares of Common Stock issued to certain shareholders of Sarborg Limited pursuant to the Securities Purchase Agreement dated July 30, 2026, (vii) 33,582 shares of Common Stock issued to NJS Foresight Bio-Advisory LLC on July 31, 2026 as consideration for services provided to the Company, (viii) 33,582 shares of Common Stock issued to Thesprogen, PC on July 31, 2026 as consideration for services provided to the Company, and (ix) 650,000 shares of Common Stock issued to Sarborg pursuant to Amendment No. 1, dated August 31, 2026, to the Securities Purchase Agreement, dated February 19, 2026.

In connection with this opinion letter, we have examined and relied upon the Registration Statement, relevant transaction documents, the Company’s certificate of incorporation (as amended and/or restated to date) and the Company’s bylaws (as amended and/or restated to date), each as currently in effect, a certificate of good standing issued by the Secretary of State of Delaware as of a recent date, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda, and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below.

In such examination and in rendering the opinion expressed below, we have assumed, without independent investigation or verification: (i) the genuineness of all signatures on all agreements, instruments, corporate records, certificates, and other documents submitted to us; (ii) the legal capacity, competency, and authority of all individuals executing documents submitted to us; (iii) the authenticity and completeness of all agreements, instruments, corporate records, certificates, and other documents submitted to us as originals; (iv) that all agreements, instruments, corporate records, certificates, and other documents submitted to us as certified, electronic, facsimile, conformed, photostatic, or other copies conform to the originals thereof, and that such originals are authentic and complete; (v) the due authorization, execution, and delivery of all agreements, instruments, corporate records, certificates and other documents by all parties thereto (other than the Company); (vi) that no documents submitted to us have been amended or terminated orally or in writing, except as has been disclosed to us in writing; and (vii) that the statements contained in the certificates and comparable documents of public officials, officers, and representatives of the Company and other persons on which we have relied for the purposes of this opinion letter are true and correct on and as of the date hereof.

300 Madison Avenue, 27th Floor New York, New York 10017

www.ThompsonHine.com O: 212.344.5680 F: 212.344.6101

We have further assumed that the appropriate action will be taken, prior to the offer and sale of the Shares by the Selling Stockholders, to register and qualify the Shares for sale under all applicable state securities or “blue sky” laws.

Based upon and subject to the foregoing, we are of the opinion that (A) the shares of Common Stock described in clauses (iii) through (ix) above are duly authorized, validly issued, fully paid, and nonassessable, and (B) the Warrant Shares and Conversion Shares will be duly authorized for issuance and, when issued, delivered and paid for in accordance with the terms of the Warrants and Notes, respectively, including the payment of the exercise price or conversion price therefor, will be validly issued, fully paid and nonassessable.

Our opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. Our opinion herein is expressed solely with respect to the federal laws of the United States and the General Corporation Law of the State of Delaware as in effect on the date hereof. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule, or regulation relating to securities, or to the sale or issuance thereof. Our opinion is based on these laws as in effect on the date hereof, and we disclaim any obligation to advise you of facts, circumstances, events, or developments which hereafter may be brought to our attention and which may alter, affect, or modify the opinion expressed herein. We express no opinion as to whether the laws of any particular jurisdiction other than those identified above are applicable to the subject matter hereof.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement, and to being named under the caption “Legal Matters” contained therein. In giving this consent, we do not hereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Thompson Hine LLP

Thompson Hine LLP