Exhibit 5.1

Sidley Austin LLP 787 Seventh Avenue New York, NY 10019 +1 212 839 5300 +1 212 839 5599 Fax   AMERICA • ASIA PACIFIC • EUROPE

May 12, 2025

GlycoMimetics, Inc.

P.O. Box 65

Monrovia, Maryland 21770

Re:         Registration Statement on Form S-4

Ladies and Gentlemen:

We refer to the Registration Statement on Form S-4 (the “Registration Statement”) being filed by GlycoMimetics, Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of up to (i) 2,423,219,696 shares of the Company’s common stock, par value $0.001 per share (the “Common Stock”), (ii) 308,384 shares of the Company’s Series A Non-Voting Convertible Preferred Stock, par value $0.001 per share (the “Preferred Stock”), (iii) 278,010,526 pre-funded warrants to purchase shares of Common Stock (the “Warrants”), (iv) 359,204,314 options to purchase shares of Common Stock (the “Options”), and (v) restricted stock units with respect to 46,779,077 shares of Common Stock (“RSUs” and, together with the securities described in clauses (i)–(iv), the “Registered Securities”), in each case subject to adjustment based on the final exchange ratio described in the Registration Statement. The Registered Securities are to be issued pursuant to the terms of the Agreement and Plan of Merger and Reorganization, dated as of October 28, 2024, as amended on February 14, 2025 and April 28, 2025 (the “Merger Agreement”), by and among the Company, Gemini Merger Sub Corp., a Delaware corporation and wholly-owned subsidiary of the Company (“First Merger Sub”), Gemini Merger Sub II, LLC, a Delaware limited liability company and wholly-owned subsidiary of the Company (“Second Merger Sub” and, together with First Merger Sub, the “Merger Subs”), and Crescent Biopharma, Inc., a Delaware corporation (“Crescent”) and the Securities Purchase Agreement, dated October 28, 2024, as amended and restated on February 14, 2025 (the “Securities Purchase Agreement”) among the Company, Crescent and certain investors party hereto.

GlycoMimetics, Inc.

May 12, 2025

Page 2

The Merger Agreement provides, among other things, that (i) First Merger Sub will merge with and into Crescent, with Crescent continuing as the surviving corporation (the “First Merger”), and (ii) immediately following the First Merger, Crescent will merge with and into Second Merger Sub, with Second Merger Sub continuing as the surviving entity and a wholly-owned subsidiary of the Company (the “Second Merger” and, together with the First Merger, the “Merger”). The Registered Securities consist of (a) shares of Common Stock (the “Common Shares”) to be issued in exchange for shares of common stock, $0.0001 par value per share, of Crescent (the “Crescent Common Stock”) pursuant to the Merger Agreement, (b) shares of Common Stock issuable upon conversion of the Preferred Stock to be issued in exchange for shares of Series Seed Convertible Preferred Stock, par value $0.0001 per share, of Crescent (the “Crescent Preferred Stock”) pursuant to the Merger Agreement (such Common Stock, the “Preferred Conversion Shares”), (c) shares of Common Stock issuable upon exercise of the Warrants to be issued in exchange for pre-funded warrants to purchase shares of Crescent common stock (the “Crescent Warrants”) pursuant to the Merger Agreement (such Common Stock, the “Warrant Shares”), (d) shares of Common Stock issuable upon exercise of the Options to be issued in exchange for options to purchase shares of Crescent common stock (the “Crescent Options”) pursuant to the Merger Agreement (such Common Stock, the “Option Shares”), (e) shares of Common Stock issuable upon settlement of RSUs to be issued in exchange for restricted stock units settleable in shares of Crescent common stock (the “Crescent RSUs”) pursuant to the Merger Agreement (such Common Stock, the “RSU Shares”), (f) shares of Preferred Stock to be issued in exchange for shares of Crescent Preferred Stock pursuant to the Merger Agreement, (g) Warrants to be issued in exchange for Crescent Warrants pursuant to the Merger Agreement, (h) Options to be issued in exchange for Crescent Options pursuant to the Merger Agreement and (i) RSUs to be issued in exchange for Crescent RSUs pursuant to the Merger Agreement.

The Merger is subject to satisfaction or waiver of a number of conditions, including approval by the stockholders of the Company of amendments to the Company’s certificate of incorporation increasing the total number of shares of authorized Common Stock and effecting a reverse stock split of issued and outstanding Common Stock at a ratio in the range of 70:1 to 110:1 (collectively, the “Charter Amendments”).

This opinion letter is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

We have examined the Registration Statement, the Merger Agreement, the Securities Purchase Agreement, the Company’s certificate of incorporation and the resolutions adopted by the board of directors of the Company relating to the Registration Statement, the Merger Agreement, the Securities Purchase Agreement, the Charter Amendments, and the issuance of the Registered Securities by the Company. We have also examined originals, or copies of originals certified to our satisfaction, of such agreements, documents, certificates and statements of the Company and other corporate documents and instruments, and have examined such questions of law, as we have considered relevant and necessary as a basis for this opinion letter. We have assumed the authenticity of all documents submitted to us as originals, the genuineness of all signatures, the legal capacity of all persons and the conformity with the original documents of any copies thereof submitted to us for examination. As to facts relevant to the opinions expressed herein, we have relied without independent investigation or verification upon, and assumed the accuracy and completeness of, certificates, letters and oral and written statements and representations of public officials and officers and other representatives of the Company.

GlycoMimetics, Inc.

May 12, 2025

Page 3

Based on the foregoing, we are of the opinion that when (i) the Registration Statement, as finally amended, shall have become effective under the Securities Act, (ii) the issuance of the Registered Securities and the Charter Amendments shall have been approved by the stockholders of the Company, (iii) the certificates of amendment to the Company’s certificate of incorporation reflecting the Charter Amendments shall have been filed in accordance with the General Corporation Laws of the State of Delaware (“DGCL”), and (iv) the Merger shall have become effective under the DGCL:

(i)            the Common Shares have been duly authorized and, upon issuance and delivery in exchange for the shares of Crescent Common Stock in accordance with the terms of the Merger Agreement, the Common Shares will be validly issued, fully paid and non-assessable;

(ii)           the Preferred Conversion Shares have been duly authorized and, assuming such Preferred Conversion Shares were issued and delivered today in accordance with the terms of the Preferred Stock upon conversion, the Preferred Conversion Shares would be validly issued, fully paid and non-assessable;

(iii)         the Warrant Shares have been duly authorized and, assuming such Warrant Shares were issued and delivered today in accordance with the terms of the Warrants upon exercise, the Warrant Shares would be validly issued, fully paid and non-assessable;

(iv)         the Option Shares have been duly authorized and, assuming such Option Shares were issued and delivered today in accordance with the terms of the Options upon exercise, the Options Shares would be validly issued, fully paid and non-assessable;

(v)           the RSU Shares have been duly authorized and, assuming such RSU Shares were issued and delivered today in accordance with the terms of the RSUs upon settlement, the RSU Shares would be validly issued, fully paid and non-assessable;

(vi)         the shares of Preferred Stock have been duly authorized and, upon issuance and delivery in exchange for the Crescent Preferred Stock in accordance with the terms of the Merger Agreement, the shares of Preferred Stock will be validly issued, fully paid and non-assessable;

(vii)        the Warrants have been duly authorized by the Company and, when executed by the Company and delivered in exchange for the Crescent Warrants in accordance with the terms of the Merger Agreement, the Warrants will be valid and binding obligations of the Company;

(viii)        the Options have been duly authorized by the Company and, when executed by the Company and delivered in exchange for the Crescent Options in accordance with the terms of the Merger Agreement, the Options will be valid and binding obligations of the Company; and

(ix)          the RSUs have been duly authorized by the Company and, when executed by the Company and delivered in exchange for the Crescent RSUs in accordance with the terms of the Merger Agreement, the RSUs will be valid and binding obligations of the Company.

The opinion expressed herein is expressed as of the date hereof and we assume no obligation to advise you of changes in law, fact or other circumstances (or the effect thereof on such opinion) that may come to our attention after such date.

Our opinions are subject to bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, fraudulent transfer and other similar laws relating to or affecting creditors' rights generally and to general equitable principles (regardless of whether considered in a proceeding in equity or at law), including concepts of commercial reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief.

GlycoMimetics, Inc.

May 12, 2025

Page 4

We hereby consent to the filing of this opinion letter as an Exhibit to the Registration Statement and to all references to our Firm included in or made a part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.