Exhibit 5.1

Skadden, Arps, Slate, Meagher & Flom llp

One Manhattan West

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

Ladies and Gentlemen:

We have acted as special United States counsel to Applied Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the Company’s sale of up to $75,000,000 aggregate gross sales price of shares (the “Securities”) of common stock, par value $0.0001 per share of the Company, pursuant to the Sales Agreement, dated August 11, 2023, between Leerink Partners LLC, as agent and the Company (the “Sales Agreement”).

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 opinion stated herein, we have examined and relied upon the following:

(a)               the registration statement on Form S-3 (File No. 333-271887) of the Company relating to the Securities and other securities of the Company filed with the Securities and Exchange Commission (the “Commission”) on May 12, 2023 under the Securities Act allowing for delayed offerings pursuant to Rule 415 of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”), including information deemed to be a part of the registration statement pursuant to Rule 430B of the Rules and Regulations and the Notice of Effectiveness of the Commission posted on its website declaring such registration statement effective on May 19, 2023 (such registration statement, as so amended, being hereinafter referred to as the “Registration Statement”);

Applied Therapeutics, Inc.

August 11, 2023

Page 2

(b)               the prospectus, dated May 19, 2023 (the “Base Prospectus”), which forms a part of and is included in the Registration Statement;

(c)                the prospectus supplement, dated August 11, 2023 (together with the Base Prospectus, the “Prospectus Supplement”), relating to the offering of the Securities, in the form filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations;

(d)               an executed copy of the Sales Agreement;

(e)               an executed copy of a certificate of Shoshana Shendelman, Secretary of the Company, dated the date hereof (the “Secretary’s Certificate”);

(f)                a copy of the Company’s Amended and Restated Certificate of Incorporation (the “Certificate of Incorporation”), certified by the Secretary of State of the State of Delaware, as of the date hereof and certified pursuant to the Secretary’s Certificate;

(g)               a copy of the Company’s Amended and Restated Bylaws (the “Bylaws”), as amended and in effect as of the date hereof, certified pursuant to the Secretary’s Certificate; and

(h)               a copy of certain resolutions of the Board of Directors of the Company, adopted on May 12, 2023 and August 10, 2023, certified pursuant to the Secretary’s Certificate.

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 opinion stated below, including the factual representations and warranties contained in the Sales Agreement.

In our examination, we have assumed the genuineness of all signatures, including electronic signatures, 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 Securities 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 Certificate of Incorporation, the 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 Statement or the Company’s Annual Report on Form 10-K for the year ended December 31, 2022). As to any facts relevant to the opinion 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 facts and conclusions set forth in the Secretary’s Certificate and the factual representations and warranties contained in the Sales Agreement.

Applied Therapeutics, Inc.

August 11, 2023

Page 3

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) certificates in the form required under the DGCL representing the Securities are duly executed and countersigned by the transfer agent; and (ii) the Securities are registered in the Company’s share registry and delivered upon payment of the consideration therefor determined by the Board of Directors, the Securities, when issued and sold in accordance with the provisions of the Sales 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. We also hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K being filed on the date hereof and incorporated by reference into 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.