Exhibit 5.1

January 23, 2020

Applied Therapeutics, Inc.
545 5th Avenue, Suite 1400
New York, NY 10173

Re:                                                     Applied Therapeutics, Inc.

Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as special counsel to Applied Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the public offering by the Company of up to 2,587,500 shares of common stock, par value $0.0001 per share (“Common Stock”), of the Company (including up to 337,500 shares of Common Stock subject to an over-allotment option) (the “Shares”).

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933 (the “Securities Act”).

In rendering the opinions stated herein, we have examined and relied upon the following:

(a)                                 the registration statement on Form S-1 (File No. 333-235988), relating to the Shares of the Company, filed on January 21, 2020 with the Securities and Exchange Commission (the “Commission”) under the Securities Act and Pre-Effective Amendment No. 1 thereto, including the information deemed to be a part of the registration statement pursuant to Rule 430A of the Rules and Regulations (such registration statement, as so amended, being hereinafter referred to as the “Registration Statement”);

(b)                                 the prospectus, dated January 23, 2020 (the “Prospectus”), which forms a part of and is included in the Registration Statement;

(c)                                  the form of the Underwriting Agreement (the “Underwriting Agreement”) proposed to be entered into between the Company and Goldman Sachs & Co. LLC, Cowen and Company, LLC and UBS Securities LLC representatives of the several Underwriters named therein (the “Underwriters”), relating to the sale by the Company to the Underwriters of the Shares, filed as Exhibit 1.1 to the Registration Statement;

(d)                                 a copy of the Company’s Amended and Restated Certificate of Incorporation, filed as Exhibit 3.1 to the Registration Statement (the “Amended and Restated Certificate of Incorporation”);

(e)                                  a copy of the Company’s Amended and Restated Bylaws, filed as Exhibit 3.2 to the Registration Statement (the “Amended and Restated Bylaws”) and

(f)                                   a copy of certain resolutions of the Board of Directors of the Company, adopted on January 19, 2020.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions stated below, including the factual representations and warranties contained in the Underwriting Agreement.

In our examination, we have assumed the genuineness of all signatures, including endorsements, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified or photocopied copies, and the authenticity of the originals of such copies.  With respect to our opinion set forth below, we have assumed that the issuance of the Shares will not violate or conflict with any agreement or instrument binding on the Company (except that we do not make this assumption with respect to the Amended and Certificate of Incorporation, the Amended and Restated Bylaws or those agreements or instruments expressed to be governed by the laws of the State of New York which are listed in Part II of the Registration). As to any facts relevant to the opinions stated herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials, including the factual representations and warranties set forth in the Underwriting Agreement.

We do not express any opinion with respect to the laws of any jurisdiction other than the General Corporation Law of the State of Delaware (the “DGCL”).

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that when (i) the Registration Statement, as finally amended (including all necessary post-effective amendments), has become effective under the Securities Act; (ii) the Underwriting Agreement has been duly authorized, executed and delivered by the Company and the other parties thereto, (iii) the Board of Directors of the Company, including any appropriate committee appointed thereby, has taken all necessary corporate action to approve the issuance and sale of the Shares and related matters, including the price per share of the Shares; (iv) certificates in the form required under the DGCL representing the Shares are duly executed and countersigned by the transfer agent; and (v) the Shares are registered in the Company’s share registry and delivered upon payment of the consideration therefor determined by the Board of Directors, the Shares, when issued and sold in accordance with the provisions of

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the Underwriting Agreement, will be duly authorized by all requisite corporate action on the part of the Company under the DGCL and validly issued, fully paid and nonassessable, provided that the consideration therefor is not less than $0.0001 per Share.

We hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus forming part of the Registration Statement.  We also hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement.  In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations.

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