Exhibit 5.1

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August 14, 2025

Aquestive Therapeutics, Inc.

30 Technology Drive

Warren, NJ 07922

Re: Prospectus Supplement to Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Aquestive Therapeutics, Inc. a Delaware corporation (the “Company”), in connection with the issuance and sale by the Company of up to 21,250,000 shares (the “Shares”) of its common stock, par value $0.001 per share (“Common Stock”), pursuant to the Registration Statement on Form S-3 (File No. 333-278498) (the “Registration Statement”), including a base prospectus, which was originally filed with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), on April 3, 2024, and was declared effective on April 23, 2024, and the related Prospectus (as defined below). The final prospectus supplement, dated August 14, 2025, relating to the Shares was filed with the Commission pursuant to Rule 424(b) under the Act on August 14, 2025 (together with the base prospectus, the “Prospectus”). All of the Shares are to be sold by the Company as described in the Registration Statement and the Prospectus.

This opinion letter is being furnished to the Company in accordance with the requirements of Item 601(b)(5) under Regulation S-K of the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement, other than as to the validity of the Shares as set forth below.

In rendering this opinion (this “Opinion”), we have examined originals or copies (in each case signed, certified or otherwise proven to our satisfaction to be genuine) of: (i) the Registration Statement and the Prospectus; (ii) the Company’s Amended and Restated Certificate of Incorporation, as filed with the Secretary of State of the State of Delaware on July 27, 2018; (iii) the Company’s Amended and Restated Bylaws, effective as of July 24, 2018; (iv) a Certificate of Good Standing with respect to the Company issued by the Secretary of State of the State of Delaware, as of a recent date; (v) the Underwriting Agreement, dated August 14, 2025, by and between the Company and Leerink Partners LLC, Cantor Fitzgerald & Co. and Oppenheimer & Co. Inc., on behalf of themselves and as representatives of the several underwriters to be included in such underwriting agreement (the “Underwriting Agreement”); and (vi) resolutions of the board of directors and a committee thereof of the Company, evidencing corporate action of the Company authorizing the issuance and sale of the Shares.

Aquestive Therapeutics, Inc. August 14, 2025 Page 2

As to the facts upon which this opinion is based, we have relied, to the extent we deem proper, upon certificates of public officials and certificates and written statements of agents, officers, directors, employees and representatives of, and accountants for, the Company and we have assumed in this regard the truthfulness of such certifications and statements. We have not independently established the facts so relied on.

In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as original documents, and the conformity to original documents of all documents submitted to us as copies, the legal capacity of natural persons who are signatories to the documents examined by us, and the legal power and authority of all persons signing on behalf of parties (other than the Company) to all documents.

We have further assumed that the Shares will be issued and sold in the manner stated in the Registration Statement and the Prospectus, and in compliance with the applicable provisions of the Act and the rules and regulations of the Commission thereunder and the securities or “Blue Sky” laws of various states and the terms and conditions of the Underwriting Agreement.

Based upon and subject to the foregoing, we are of the opinion that, as of the date hereof, (i) the Shares have been duly authorized for issuance by the Company and (ii) the Shares, when duly registered on the books of the transfer agent and registrar in the name and on behalf of the purchasers and when issued and sold by the Company and delivered against payment therefor in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and non-assessable.

Our opinions set forth herein are based solely upon the laws of the State of New York and the General Corporation Law of the State of Delaware as in effect on the date hereof, and we express no opinion with respect to any other laws, rules or regulations (including, without limitation, the application of the securities or “Blue Sky” laws of any state to the offer and/or sale of the Shares).

We hereby consent to the filing of this Opinion as an exhibit to the Company’s Current Report on Form 8-K filed with the Commission on August 14, 2025 and as an exhibit to any application under the securities or other laws of any state of the United States which relate to the offer and sale of the Shares. We further consent to the use of our name under the heading “Legal Matters” and the Prospectus related to the Registration Statement. In giving this consent, we do not admit hereby that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.

Aquestive Therapeutics, Inc. August 14, 2025 Page 3

This Opinion is furnished to you in connection with the closing of the offer and sale of the Shares and is not to be used, circulated, quoted or otherwise relied upon for any other purpose, except as expressly provided in the preceding paragraph. This Opinion is furnished as of the date hereof and we disclaim any undertaking to update this Opinion after the date hereof or to advise you of any subsequent changes of the facts stated or assumed herein or of any subsequent changes in applicable law.

Very truly yours,

/s/ Dechert LLP

Dechert LLP