Exhibit 5.1

DuMoulin Black LLP 10th Floor 595 Howe Street Vancouver BC Canada V6C 2T5 www.dumoulinblack.com   Telephone No. (604) 687-1224

File No. 5653-002

February 10, 2026

Austin Gold Corp.
1021 West Hastings Street, 9^th Floor
Vancouver, B.C. V6C 0C3

Dear Sirs/Mesdames:

We have acted as counsel in British Columbia (the “Province”) to the Company, which is a corporation incorporated pursuant to the laws of the Province, with respect to certain legal matters in connection with the registration by the Company, under the U.S. Securities Act of 1933, as amended, of the offer and sale by the Company in the United States of its common shares, having an aggregate offering price of up to US$7,500,000 pursuant to an At the Market Offering Agreement dated August 22, 2025 (the “ATM Agreement”) by and between the Company and H.C. Wainwright & Co., LLC (the “Lead Manager”) and Roth Capital Partners (together with the Lead Manager, the “Managers”). The Company has filed a prospectus supplement (the “Prospectus Supplement that relates to the offer (the “Offering”) of up to US$7,500,000 of the Company’s common shares (the “Shares”) pursuant to the Company’s base prospectus under its registration statement on Form F-3 of which the Prospectus Supplement forms a part (the “Registration Statement”).

In connection with rendering this opinion, we have examined originals, certified copies or copies otherwise identified as being true copies of the following: 

(a) the articles of the Company, as in effect on the date hereof and as amended to date; 

(b) a copy of the resolutions passed by the directors of the Company, among other things, authorizing the Offering, the execution and delivery of the ATM Agreement and the issuance of the Shares; and

(c) such other instruments and documents as we have deemed relevant or necessary in connection with our opinions set forth herein.

We have considered such questions of law, made such investigations and examined such originals, facsimiles or copies, certified or otherwise identified to our satisfaction, of such additional public and corporate records, records of corporate proceedings, certificates and other documents as we have considered relevant or necessary in order to render the opinions expressed below.

We are solicitors qualified to practice law in the Province only and we express no opinion as to the laws of any jurisdiction, or as to any matters governed by the laws of any jurisdiction, other than the laws of the Province and the laws of Canada applicable therein. The opinions herein are based on the laws of the Province and the laws of Canada applicable therein in effect on the date hereof.

The opinions herein are given as of the date of this letter and are not prospective. We disclaim any obligation to advise the addressees or any other person of any change in law (whether by legislative action, judicial decision or otherwise) or changes in any fact which may come or be brought to our attention after the date of this letter.

We have also examined and relied upon such other documents as we have deemed relevant and necessary as a basis for the opinions hereinafter expressed. We have assumed the genuineness of all signatures, the legal capacity at all relevant times of any individual signing such documents, the authenticity and completeness of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as certified or photostatic copies or facsimiles (including scanned copies provided by email), and the authenticity of the originals of such certified or photostatic copies or facsimiles and the truth and accuracy of all corporate records of the Company and certificates of officers provided to us by the Company.

Whenever our opinion refers to shares of the Company whether issued or to be issued, as being “fully paid and non-assessable”, such opinion indicates that the holder of such shares will not be liable to contribute any further amounts to the Company by virtue of its status as a holder of such shares, either in order to complete payment for the shares or to generally satisfy claims of creditors of the Company. No opinion is expressed as to actual receipt by the Company of the consideration for the issuance of such shares or as to the adequacy of any consideration received.

Based and relying upon and subject to the foregoing and the qualifications hereinafter expressed, we are of the opinion that at the date hereof, the Shares have been duly allotted and authorized for issue by the Company and when issued and paid for in accordance with the ATM Agreement, and upon receipt by the Company of full payment for each Share, the Shares will be validly issued as fully paid and non-assessable shares.

We hereby consent to the filing of this opinion with the Securities Exchange Commission (the “SEC”) as an exhibit to the Registration Statement to be filed by the Company in connection with the Offering. We also hereby consent to the use of our name under the heading “Legal Matters” in the Registration Statement and Prospectus Supplement which forms part of 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 Act or the rules and regulations of the SEC promulgated thereunder.

Yours truly,

/s/ Dumoulin Black LLP