Exhibit 5.1

Brent B. Siler

T: +1 703 456 8058

bsiler@cooley.com

January 7, 2014

GlycoMimetics, Inc.

401 Professional Drive, Suite 250

Gaithersburg, Maryland 20879

Ladies and Gentlemen:

You have requested our opinion with respect to certain matters in connection with the filing by GlycoMimetics, Inc., a Delaware corporation (the “Company”) of a Registration Statement (No. 333-191567) on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus filed with the Registration Statement (the “Prospectus”), covering an underwritten public offering of up to 6,612,500 shares of common stock (the “Shares”), including 862,500 shares for which the underwriters have been granted an option to purchase.

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and related Prospectus, (b) the Company’s Amended and Restated Certificate of Incorporation, as amended to date and as currently in effect, filed as Exhibits 3.1 and 3.2 to the Registration Statement, (c) the Company’s Bylaws, as amended to date and as currently in effect, filed as Exhibit 3.4 to the Registration Statement, (d) the Company’s Amended and Restated Certificate of Incorporation, filed as Exhibit 3.3 to the Registration Statement, which will be in effect upon the closing of the offering contemplated by the Registration Statement, (e) the Company’s Amended and Restated Bylaws, filed as Exhibit 3.5 to the Registration Statement, which will be in effect upon the closing of the offering contemplated by the Registration Statement, and (f) 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. We have assumed the genuineness and authenticity of all documents submitted to us as originals and the conformity to originals of all documents where due execution and delivery are a prerequisite to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of officers of the Company and have not sought to independently verify such matters. Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares have been duly authorized by the Company and, when sold and issued in accordance with the Registration Statement and the related Prospectus, will be validly issued, fully paid and non-assessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus included in the Registration Statement and to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,

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