Exhibit 5.1

[Letterhead of Wachtell, Lipton, Rosen & Katz]

November 3, 2025

National Bank Holdings Corporation
7800 East Orchard Road, Suite 300
Greenwood Village, Colorado 80111

Re: Registration Statement on Form S-4 (File No. 333-290938)

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-4 (as amended, the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”), relating to the registration under the Securities Act of 1933, as amended (the “Securities Act”), of up to 7,381,361 shares of Class A common stock, par value $0.01 per share, of NBHC (the “Common Shares”) to be issued in connection with the merger contemplated by the Agreement and Plan of Merger (the “Merger Agreement”), dated as of September 15, 2025, by and among NBHC, Vista Bancshares, Inc., a Texas Corporation (“Vista”), and Bryan Wick, solely in his capacity as the shareholders’ representative, pursuant to which Vista will merge with and into NBHC (the “Merger”), with NBHC as the surviving corporation.

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 Merger Agreement; (iii) the Second Amended and Restated Certificate of Incorporation of NBHC; and (iv) the Second Amended and Restated Bylaws of NBHC, which collectively we refer to herein as the “Transaction Documents”. 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 also assumed the valid authorization, execution and delivery of each of the Transaction Documents by each party thereto (other than NBHC), and we have assumed that each such other party (in the case of parties which are not natural persons) has been duly organized and is validly existing and in good standing under its jurisdiction of organization, that each such other party has the legal capacity, power and authority to perform its obligations thereunder and that each of the Transaction Documents constitutes the valid and binding obligation of all such other parties, enforceable against them in accordance with its terms.

We have not considered, and we express no opinion as to, any law other than the laws of the State of New York and 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.

November 3, 2025

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 to be issued by NBHC pursuant to and in the manner contemplated by the terms of the Merger Agreement will be, upon issuance, duly authorized and, when the Registration Statement has been declared effective by order of the Commission and the Common Shares have been issued and delivered in the manner contemplated by and upon the terms and conditions set forth in the Registration Statement and the Merger Agreement, such 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, including, without limitation, the enforceability of the governing law provision contained in the Transaction Documents or in any other agreement.

We hereby consent to be named in the Registration Statement and in the related proxy statement/prospectus contained therein as attorneys who passed upon the legality of the Common Shares to be issued pursuant to the Registration Statement and to the filing of a copy of this opinion as Exhibit 5.1 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.