Exhibit 5.1

July 8, 2026

AEON Biopharma, Inc.

5 Park Plaza, Suite 1750

Irvine, CA 92614

Ladies and Gentlemen:

We have acted as special counsel to AEON Biopharma, Inc., a Delaware corporation (the “Company”), in connection with its Registration Statement on Form S-1, as amended (the “Registration Statement”), initially filed with the U.S. Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”), on July 8, 2026, related to the proposed public offering of $14,375,000 in securities (inclusive of $1,875,000 in respect of the over-allotment securities), consisting of up to (i) shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”) or pre-funded warrants to purchase shares of Common Stock in lieu thereof (the “Pre-Funded Warrants”), along with (ii) two-year milestone warrants to purchase shares of Common Stock (the “Two-Year Milestone Warrants”) and (iii) five-year milestone warrants to purchase shares of Common Stock (the “Five-Year Milestone Warrants”, together with the Two-Year Milestone Warrants, the “Milestone Warrants”). The Registration Statement also covers the shares of Common Stock underlying the Pre-Funded Warrants, the Two-Year Milestone Warrants and the Five-Year Milestone Warrants (collectively, the “Warrant Shares”). The Shares, the Pre-Funded Warrants, the Milestone Warrants and the Warrant Shares are collectively referred to herein as the “Securities.”

The Securities will be offered and sold pursuant to the Registration Statement and an underwriting agreement (the “Underwriting Agreement”) to be entered into by and between the Company and Lake Street Capital Markets, LLC, as representative of the several underwriters named therein (the “Representative”).

As counsel to the Company in connection with the proposed issuance and sale of the Securities, we have examined: (i) the Company’s certificate of incorporation, as amended and restated, and bylaws, as amended and restated, each as currently in effect; (ii) certain resolutions of the Company’s board of directors relating to the issuance and sale of the Securities; (iii) the form of Underwriting Agreement; (iv) the form of Warrant Agency Agreement to be entered into between the Company and Continental Stock Transfer & Trust Company, as warrant agent (in such capacity, the “Warrant Agent”); (v) the form of Two-Year Milestone Warrant; (vi) the form of Five-Year Milestone Warrant; (vii) the form of Pre-Funded Warrant; (viii) the Registration Statement; and (ix) such other proceedings, documents, and records as we have deemed necessary to enable us to render this opinion. In all such examinations, we have assumed the genuineness of all signatures, the authenticity of all documents, certificates, and instruments submitted to us as originals, and the conformity with the originals of all documents, certificates, and instruments submitted to us as copies. We have also assumed the due execution and delivery of all documents where due execution and delivery are prerequisite to the effectiveness thereof.

Our opinions set forth below with respect to the validity or binding effect of any security or obligation may be limited by (i) bankruptcy, insolvency, reorganization, fraudulent conveyance, marshaling, moratorium or other similar laws affecting the enforcement generally of the rights and remedies of creditors and secured parties or the obligations of debtors, (ii) general principles of equity (whether considered in a proceeding in equity or at law), including but not limited to principles limiting the availability of specific performance or injunctive relief, and concepts of materiality, reasonableness, good faith and fair dealing, (iii) the possible unenforceability under certain circumstances of provisions providing for indemnification, contribution, exculpation, release or waiver that may be contrary to public policy or violative of federal or state securities laws, rules or regulations, and (iv) the effect of course of dealing, course of performance, oral agreements or the like that would modify the terms of an agreement or the respective rights or obligations of the parties under an agreement.

Based upon, subject to and limited by the foregoing, we are of the opinion that, following (i) execution and delivery by the Company and the Representative of the Underwriting Agreement, (ii) execution and delivery by the Company and the Warrant Agent of the Warrant Agency Agreement, (iii) execution and delivery by the Company of the Pre-Funded Warrants, the Two-Year Milestone Warrants and the Five-Year Milestone Warrants, (iv) countersignature of the Pre-Funded Warrants, the Two-Year Milestone Warrants and the Five-Year Milestone Warrants by the Warrant Agent in accordance with the terms of the Warrant Agency Agreement, (v) effectiveness of the Registration Statement, (vi) issuance of the Securities pursuant to the terms of the Underwriting Agreement, and (vii) the receipt by the Company of the applicable consideration for the Securities:

(i) the Securities have been duly authorized for issuance;

(ii) the Shares, when issued, delivered and paid for in accordance with the terms of the Underwriting Agreement and in accordance with and in the manner described in the Registration Statement, will be validly issued, fully paid and nonassessable shares of Common Stock;

(iii) each of the Pre-Funded Warrants, the Two-Year Milestone Warrants and the Five-Year Milestone Warrants (collectively, the “Warrants”), when duly executed and delivered by the Company and countersigned by the Warrant Agent in accordance with the terms of the Warrant Agency Agreement and delivered against payment therefor in accordance with the terms of the Underwriting Agreement and in accordance with and in the manner described in the Registration Statement, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms; and

(iv) the Warrant Shares, when issued, delivered and paid for in accordance with the terms of the Milestone Warrants or the Pre-Funded Warrants, as applicable, will be validly issued, fully paid and non-assessable shares of Common Stock.

It is understood that this opinion is to be used only in connection with the offer, sale, and issuance of the Securities while the Registration Statement is in effect.

This opinion speaks only as of the date hereof and we assume no obligation to update or supplement this opinion if any applicable laws change after the date of this opinion or if we become aware after the date of this opinion of any facts, whether existing before or arising after the date hereof, that might change the opinions expressed above. This opinion is furnished in connection with the filing of the Registration Statement and may not be relied upon for any other purpose without our prior written consent in each instance. Further, no portion of this opinion may be quoted, circulated or referred to in any other document for any other purpose without our prior written consent.

We hereby consent to the filing of this opinion with the SEC as Exhibit 5.1 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the Registration Statement. In giving such consent, we do not thereby admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the SEC promulgated thereunder.