Exhibit 5.1

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October 23, 2026

Alchemy Acquisition Holdings, Inc.

850 Library Avenue, Suite 204-F

Newark, Delaware 19711

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Ladies and Gentlemen:

We have acted as United States securities counsel to Alchemy Acquisition Holdings, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-4 initially filed by the Company with the Securities and Exchange Commission (the “Commission”) on October 23, 2026 under the Securities Act of 1933, as amended (the “Act”). Such Registration Statement, as amended or supplemented, is hereinafter referred to as the “Registration Statement”. The Company has entered into a Business Combination Agreement, dated as of August 22, 2025 (the “Business Combination Agreement”), by and among the Company, Alchemy Investments Acquisition Corp 1, a Cayman Islands exempted company and the parent of the Company (“Parent”), Alchemy Merger Sub, LLC, a Delaware limited liability company and wholly-owned subsidiary of the Company (“Newco”), Cartiga, LLC, a Delaware limited liability company (“Cartiga”), and Halle Benett, as the Sellers’ Representative. Pursuant to the Business Combination Agreement, at least one Business Day prior to the Closing Date (each as defined in the Business Combination Agreement), Parent will re-domicile as a Delaware corporation by means of a merger of Parent with and into the Company, with the Company surviving the merger and changing its name to “Cartiga Holdings, Inc.” (the “Domestication Merger”). Thereafter, at the Closing, Newco will merge with and into Cartiga, with Cartiga surviving the merger under the Delaware Limited Liability Company Act and the Company becoming its sole managing member (the “Merger” and, together with the Domestication Merger, the “Business Combination”). The Domestication Merger is subject to the approval of the shareholders of Parent.

Upon the effectiveness of the Domestication Merger, among other things, (i) each issued and outstanding Class A ordinary share, par value $0.0001 per share, of Parent (the “Class A Ordinary Shares”) will convert into one share of Class A common stock, par value $0.0001 per share, of the Company (the “Class A Common Stock”), (ii) each issued and outstanding Class B ordinary share, par value $0.0001 per share, of Parent will be converted into one share of Class B common stock, par value $0.0001 per share, of the Company (the “Class B Common Stock”), (iii) each issued and outstanding unit of Parent, consisting of one Class A Ordinary Share and one-half of one warrant of Parent, will be separated into its component Class A Ordinary Share and one-half of one warrant of Parent, which will convert as provided in clauses (i) and (iv), (iv) each issued and outstanding warrant of Parent (the “Warrants”), issued

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For the United States offices, a limited liability partnership including professional corporations. For Hong Kong office, a limited liability partnership.

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pursuant to that certain Warrant Agreement, dated May 4, 2023, by and between Parent and Continental Stock Transfer & Trust Company, as warrant agent (the “Warrant Agreement”), will convert into a warrant of the Company entitling the holder to purchase one share of Class A Common Stock at an exercise price of $11.50 per share, subject to adjustment (the “Company Warrants”). Immediately prior to the Effective Time (as defined in the Business Combination Agreement), the Company will adopt its amended and restated certificate of incorporation and bylaws, providing for Class A Common Stock and Class B Common Stock. Following the Merger, the Company will not have any units outstanding.

This opinion is being rendered in connection with the registration under the Registration Statement of up to (i) 3,659,056 shares of Class A Common Stock issuable upon conversion of the issued and outstanding Class A Ordinary Shares (including Class A Ordinary Shares underlying units of Parent) in the Domestication Merger (the “Conversion Shares”) and (ii) 5,750,000 Company Warrants issuable upon conversion of the warrants underlying units of Parent.

We have examined such documents and considered such legal matters as we have deemed necessary and relevant as the basis for the opinions set forth below. With respect to such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as reproduced or certified copies, and the authenticity of the originals of those latter documents. As to questions of fact material to this opinion, we have, to the extent deemed appropriate, relied upon representations of certain officers of the Company.

Based upon the foregoing, we are of the opinion that:

1. Upon the effectiveness and closing of the Domestication Merger and the conversion and separation described above, the Conversion Shares will be validly issued, fully paid and non-assessable.

2. Upon the effectiveness and closing of the Domestication Merger and the conversion and separation described above, each issued and outstanding Company Warrant will be a valid and binding agreement of the Company, enforceable against the Company in accordance with its terms.

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. In addition, we have assumed that (i) the Domestication Merger will be duly authorized, approved and registered in accordance with the Companies Act (As Revised) of the Cayman Islands and the General Corporation Law of the State of Delaware (the “DGCL”), (ii) the effectiveness of the Domestication Merger will result in the Company assuming all rights, duties and obligations of Parent under the Warrant Agreement, and (iii) at the time of issuance of the Conversion Shares and upon any exercise of the Company Warrants, the Company’s certificate of incorporation then in effect will authorize a sufficient number of shares of Class A Common Stock.

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The opinion set forth in paragraph 2 above is 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 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 or (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 applicable provisions of the DGCL. We express no opinion with respect to any other laws.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference made to us under the caption, “Legal Matters,” in the Registration Statement and in the prospectus constituting a part of the Registration Statement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act, or the rules and regulations promulgated thereunder or Item 509 of Regulation S-K promulgated under the Act.

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