Exhibit 5.1

Brian F. Leaf

(703) 456-8053

bleaf@cooley.com

October 7, 2020

GlycoMimetics, Inc.

9708 Medical Center Drive

Rockville, Maryland 20850

We have represented GlycoMimetics, Inc., a Delaware corporation (the “Company”), in connection with the offering by the Company of up to $100,000,000 of the Company’s common stock, par value $0.001 per share, (the “Shares”), pursuant to a Registration Statement on Form S-3 (File No. 333-231577) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement dated October 7, 2020, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (together with the Base Prospectus, the “Prospectus”). The Shares are to be sold by the Company in accordance with the Sales Agreement dated October 7, 2020 (the “Sales Agreement”), between the Company and Cowen and Company, LLC, as described in the Prospectus.

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, (c) the Sales Agreement and (d) 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. We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies, the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents by all persons other than the Company of all documents where due authorization, execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of officers of the Company and have not independently verified such matters.

We have assumed (i) that the specific sale of Shares will be duly authorized by the Board of Directors of the Company, a duly authorized committee thereof or a person or body pursuant to an authorization granted in accordance with Section 152 of the General Corporation Law of the State of Delaware (the “DGCL”), (ii) that no more than 40,000,000 Shares will be sold and (iii) that the price at which the Shares are sold will equal or exceed the par value of the Common Stock. We express no opinion to the extent that future issuances of securities of the Company and/or anti-dilution adjustments to outstanding securities of the Company cause the number of shares of Common Stock outstanding or issuable upon conversion or exercise of outstanding securities of the Company to exceed the number of Shares then issuable under the Sales Agreement.

Our opinion is expressed only with respect to the DGCL. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing and in reliance thereon, we are of the opinion that the Shares, when issued and paid for in accordance with the Sales Agreement and as provided in the Prospectus, will be validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement.

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ONE FREEDOM SQUARE, RESTON TOWN CENTER, 11951 FREEDOM DRIVE, RESTON, VA 20190-5640 T: (703) 456-8000 F: (703) 456-8100 WWW.COOLEY.COM

October 7, 2020

Page Two

Sincerely,

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ONE FREEDOM SQUARE, RESTON TOWN CENTER, 11951 FREEDOM DRIVE, RESTON, VA 20190-5640 T: (703) 456-8000 F: (703) 456-8100 WWW.COOLEY.COM