Exhibit 5.1

[Letterhead of Wachtell, Lipton, Rosen & Katz]

January 30, 2026

National Bank Holdings Corporation

7800 East Orchard, Suite 300

Greenwood Village, Colorado 80111

Ladies and Gentlemen:

We have acted as special counsel to National Bank Holdings Corporation, a Delaware corporation ( “NBHC”), in connection with the Registration Statement on Form S-8 (as amended, the “Registration Statement”) filed with the Securities and Exchange Commission, relating to the registration under the Securities Act of 1933, as amended (the “Securities Act”), of up to 50,000 shares (the “Common Shares”) of common stock, par value $0.01 per share, of NBHC, authorized for issuance pursuant to the National Bank Holdings Corporation 2026 Inducement Plan (the “Inducement Plan”).

In connection with the opinion set forth herein, we have examined and relied on originals or copies, certified or otherwise, identified to our satisfaction, of such documents, corporate records, agreements, certificates, and other instruments and such matters of law, in each case, as we have deemed necessary or appropriate for the purposes of this opinion, including (i) the Registration Statement; (ii) the Inducement Plan; (iii) the Second Amended and Restated Certificate of Incorporation of NBHC; and (iv) the Second Amended and Restated Bylaws of NBHC. We have also conducted such investigations of fact and law as we have deemed necessary or advisable for purposes of this opinion. In such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as copies and the legal capacity of all individuals executing such documents.

We have not considered, and we express no opinion as to, any law other than the Delaware General Corporation Law (including the statutory provisions and reported judicial decisions interpreting the foregoing), in each case as in effect on the date hereof.

We have also assumed that the appropriate action will be taken, prior to the offer and sale of the Common Shares in accordance with the Inducement Plan, to register and qualify the Common Shares for sale under all applicable state securities or “blue sky” laws. We have further assumed that there will be no material changes to the documents we have examined and that, at all times prior to the issuance of the Common Shares, NBHC will maintain a sufficient number of authorized but unissued shares of common stock, par value $0.01 per share, available for such issuance.

January 30, 2026
Page 2

Based upon the foregoing and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that the Common Shares have been duly authorized for issuance and, when the Common Shares are issued in accordance with the terms and conditions of the Inducement Plan, the Common Shares will be validly issued, fully paid and nonassessable.

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally, (b) general equitable principles (whether considered in a proceeding in equity or at law) and (c) an implied covenant of good faith and fair dealing. We express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof.

We consent to the filing of a copy of this opinion 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, and the rules and regulations thereunder. This opinion speaks as of its date, and we undertake no (and hereby disclaim any) obligation to update this opinion.