Exhibit 5.1

Robert W. Phillips

+1 415 693 2020

rphillips@cooley.com

May 24, 2017

Syndax Pharmaceuticals, Inc.

Building D, Floor 3

35 Gatehouse Drive

Waltham, Massachusetts 02451

Ladies and Gentlemen:

You have requested our opinion with respect to certain matters in connection with the offering by Syndax Pharmaceuticals, Inc., a Delaware corporation (the “Company”), of up to 4,312,500 shares (the “Shares”) (including up to 562,500 shares that may be sold pursuant to the underwriters’ exercise of an option to purchase additional shares) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), pursuant to a Registration Statement on Form S-3 (Registration No. 333-217172) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the related prospectus dated April 20, 2017 (the “Base Prospectus”) and the prospectus supplement dated May 24, 2017, filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, and 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, the conformity to originals of all documents submitted to us as copies thereof, the accuracy, completeness and authenticity of certificates of public officials, and the due execution and delivery 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 an officer of the Company and have not sought independently to verify such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion as to whether the laws of any particular jurisdiction are applicable to the subject matter hereof. We are not rendering any opinion as to compliance with any federal or state law, rule or regulation relating to securities, or to the sale or issuance thereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold in accordance with the Registration Statement and the related Prospectus, will be validly issued, fully paid and nonassessable.

Cooley LLP    101 California Street    5th Floor    San Francisco, CA    94111-5800

t: (415) 693-2000    f: (415) 693-2222    cooley.com

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 a current report of the Company on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement.

Cooley LLP    101 California Street    5th Floor    San Francisco, CA    94111-5800

t: (415) 693-2000    f: (415) 693-2222    cooley.com