Exhibit 5.1

One Atlantic Center

1201 West Peachtree Street

Atlanta, GA 30309-3424

404-881-7000 | Fax: 404-881-7777

February 14, 2024

Texas Capital Bancshares, Inc.
2000 McKinney Avenue
Suite 700
Dallas, Texas 75201

Re:    Automatic Shelf Registration Statement on Form S-3ASR (the “Registration Statement”)

Ladies and Gentlemen:

We have acted as counsel to Texas Capital Bancshares, Inc., a Delaware corporation (the “Company”), in connection with the Company’s filing on the date hereof of the above-referenced Registration Statement with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”).

This opinion is being furnished pursuant to Item 16 of Form S-3 and Item 601(b)(5) of Regulation S-K under the Securities Act.

The Registration Statement relates to the proposed issuance and sale from time to time pursuant to Rule 415 under the Securities Act of the following securities: (i) shares of common stock, par value $0.01 per share, of the Company (the “Common Stock”); (ii) shares preferred stock, par value $0.01 per share, of the Company (the “Preferred Stock”); (iii) warrants (the “Warrants”); (iv) senior debt securities and subordinated debt securities (collectively, the “Debt Securities”), which may be issued pursuant to a senior debt indenture (the “Senior Debt Indenture”) between the Company and U.S. Bank National Association, as trustee (the “Senior Debt Trustee”) and a subordinated debt indenture (the “Subordinated Debt Indenture” and together with the Senior Debt Indenture, the “Indentures”) between the Company and U.S. Bank National Association, as trustee (the “Subordinated Debt Trustee” and together with the Senior Debt Trustee, the “Trustees”); (v) depositary shares to purchase fractional shares of Preferred Stock (the “Depositary Shares”), which may be issued pursuant to one or more depositary agreements (each, a “Depositary Agreement”) to be entered into between the Company and the depositary agent to be named therein (the “Depositary Agent”); (vi) purchase contracts (the “Purchase Contracts”), which may be issued under one or more purchase contract agreements (each, a “Purchase Contract Agreement”) to be entered into between the Company and the purchase contract agent to be named therein (the “Purchase Contract Agent”); and (vii) a combination of two or more securities that may be offered in the form of units (the “Units”) to be issued under one or more unit agreements (a “Unit Agreement”) to be entered into among the Company, a bank or trust company, as unit agent (the “Unit Agent”), and the holders from time to time of the Units. The Common Stock, Preferred Stock, Warrants, Debt Securities, Depositary Shares, Purchase Contracts and the Units are each referred to herein as a “Security” and are collectively referred to herein as the “Securities.”

Alston & Bird LLP         www.alston.com

February 14, 2024

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In rendering the opinions expressed herein, and except as hereinafter limited, we have considered such matters of law and of fact, including the examination of originals or copies, certified or otherwise identified to our satisfaction, of such records and documents of the Company, including the Certificate of Incorporation of the Company, as amended; the Amended and Restated Bylaws of the Company, as amended; the Registration Statement; and such records of the proceedings of the Board of Directors of the Company, including but not limited to resolutions adopted by the Board of Directors of the Company, as we deemed appropriate as a basis for the opinions hereinafter set forth. In our examination, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as original documents and the conformity to original documents submitted to us as certified, conformed, facsimile, electronic or photostatic copies.

As to certain factual matters relevant to this opinion letter, we have relied conclusively upon originals or copies, certified or otherwise identified to our satisfaction, of such records, agreements, documents and instruments, including certificates or comparable documents of officers of the Company and of public officials, as we have deemed appropriate as a basis for the opinions hereinafter set forth. Except to the extent expressly set forth herein, we have made no independent investigations with regard thereto, and, accordingly, we do not express any opinion or belief as to matters that might have been disclosed by independent verification.

This opinion is limited in all respects to the laws of the State of Delaware and the State of New York, and no opinion is expressed with respect to the laws of any other jurisdiction or any effect that such laws may have on the opinions expressed herein; provided, however, that opinion (4) below is limited to the laws of the State of New York that, in our professional judgment, are normally applicable to transactions of the type contemplated by the Indentures, and, with respect to opinion (4) below, we do not express any opinion herein concerning any other laws. This opinion is limited to the matters stated herein, and no opinion is implied or may be inferred beyond the matters expressly stated herein.

Based upon the foregoing, and subject, in all respects, to the limitations, qualifications, exceptions and assumptions set forth herein, it is our opinion that:

(1)Any shares of Common Stock, when (a) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary action to authorize the issuance of the Common Stock, (b) there are sufficient numbers of authorized but unissued shares of Common Stock, (c) the shares of Common Stock have been duly issued and delivered in accordance with the applicable underwriting agreement or other agreement approved by the Board of Directors of the Company or duly authorized committee thereof, and (d) the Company has received the consideration approved by the Board of Directors of the Company or duly authorized committee thereof for the shares of Common Stock as provided in the applicable agreement (which consideration is not less than the par value of the Common Stock), will be legally issued, fully paid and non-assessable shares of Common Stock.

(2)Any shares of Preferred Stock, when (a) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary action to authorize the issuance of the Preferred Stock, (b) there are sufficient numbers of authorized but unissued shares of Preferred Stock, (c) the shares of Preferred Stock have been duly issued and delivered in accordance with the applicable underwriting agreement or other agreement approved by the Board of Directors of the Company or duly authorized committee thereof, and (d) the Company has received the consideration approved by the Board of Directors of the Company or duly authorized committee thereof for the shares of Preferred Stock as provided in the applicable agreement (which consideration is not less than the par value of the Preferred Stock), will be legally issued, fully paid and non-assessable shares of Preferred Stock.

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(3)Any Warrants, when (a) the warrant agreement has been duly authorized, executed and delivered by the parties thereto, (b) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary corporate action to approve and establish the terms of the Warrants and to authorize and approve the issuance thereof, (c) the Warrants have been issued and delivered in accordance with the warrant agreement, applicable underwriting agreement or other agreement approved by the Board of Directors of the Company or duly authorized committee thereof and (d) the Company has received the consideration approved by the Board of Directors of the Company or duly authorized committee thereof for the Warrants as provided in the applicable agreement, will be validly issued and will constitute valid and binding obligations of the Company.

(4)Any Debt Securities, assuming the relevant Indenture has been duly authorized, executed and delivered by the Trustee and the Company, and when (a) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary corporate action to approve and establish the terms of the Debt Securities and to authorize and approve the issuance thereof, (b) any supplemental indenture, officers’ certificate or board resolution in respect of the issuance of any Debt Securities has been duly authorized, executed and delivered by the Trustee and the Company; (c) the specific terms of a particular series of Debt Securities have been duly authorized and established in accordance with the Indenture and any supplemental indenture, officers’ certificate or board resolution to be entered into or adopted in connection with the issuance of such Debt Securities; (d) such Debt Securities have been duly authorized, executed, authenticated, issued and delivered in accordance with the Indenture and any supplemental indenture, officers’ certificate or board resolution to be entered into or adopted in connection with the issuance of such Debt Securities and the applicable underwriting or other agreement; and (e) the Company has received the consideration for the Debt Securities approved by the Company as provided in the applicable indenture and other applicable agreements, will constitute valid and binding obligations of the Company, provided that we express no opinion as to (x) the effect of fraudulent conveyance, fraudulent transfer or similar provision of applicable law on the conclusions expressed above, (y) the validity or legally binding effect of any provision that permits holders to collect any portion of stated principal amount upon acceleration of the Debt Securities to the extent determined to constitute unearned interest or, (z) the applicability (and if applicable, the effect) of Section 548 of the United States Bankruptcy Code or any comparable provision of state law to the questions addressed above or on the conclusions expressed with respect thereto.

(5)Any Depositary Shares, when (a) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary corporate action to approve and establish the terms of the Depositary Shares and to authorize and approve the issuance thereof, (b) the Depositary Agreement to be entered into in connection with the issuance of any Depositary Shares has been duly authorized, executed and delivered by the Depositary Agent and the Company, (c) the specific terms of the Depositary Shares have been duly authorized and established in accordance with the Depositary Agreement, (d) such Depositary Shares have been duly issued and delivered in accordance with the Depositary Agreement and the applicable underwriting or other agreement and (e) the Company has received the consideration for the Depositary Shares approved by the Company as provided in the Depositary Agreement and other applicable agreements, such Depositary Shares will constitute valid and binding obligations of the Company.

(6)Any Purchase Contracts, when (a) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary corporate action to approve and establish the terms of the Purchase Contracts and to authorize and approve the issuance thereof, (b) the Purchase Contract Agreement to be entered into in connection with the issuance of any Purchase Contracts has been duly authorized, executed and delivered by the Purchase Contract Agent and the

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Company, (c) the specific terms of the Purchase Contracts have been duly authorized and established in accordance with the Purchase Contract Agreement, (d) such Purchase Contracts have been duly issued and delivered in accordance with the Purchase Contract Agreement and the applicable underwriting or other agreement, and (e) the Company has received the consideration for the Purchase Contracts approved by the Company as provided in the Purchase Contract Agreement and other applicable agreement, such Purchase Contracts will constitute valid and binding obligations of the Company.

(7)Any Units, when (a) the Board of Directors of the Company or a duly authorized committee thereof and the appropriate officers of the Company have taken all necessary corporate action to approve and establish the terms of the Units and to authorize and approve the issuance thereof, (b) the Unit Agreement to be entered into in connection with the issuance of any Units has been duly authorized, executed and delivered by the Unit Agent and the Company, (c) the specific terms of the Units have been duly authorized and established in accordance with the Unit Agreement, (d) such Units have been duly issued and delivered in accordance with the Unit Agreement and the applicable underwriting or other agreement, and (e) the Company has received the consideration for the Units approved by the Company as provided in the Unit Agreement and other applicable agreements, such Units will constitute valid and binding obligations of the Company.

In connection with the opinions expressed above, we have assumed that, at or prior to the time of the delivery of any such security: (i) the Board of Directors of the Company or a duly authorized committee thereof shall have duly established the terms of such security and duly authorized the issuance and sale of such security and such authorization shall not have been modified or rescinded; (ii) the Company shall remain validly existing as a corporation in good standing under the laws of the State of Delaware; (iii) the Registration Statement shall have become effective and such effectiveness shall not have been terminated or rescinded; (iv) the Indentures and the Debt Securities, the Warrant Agreement, the Depositary Agreement, the Purchase Contract Agreement and the Unit Agreement, as applicable, are each valid, binding and enforceable agreements of each party thereto (other than the Company); and (v) there shall not have occurred any change in law affecting the validity or enforceability of such security. We have also assumed that the execution, delivery and performance by the Company of any security whose terms are established subsequent to the date hereof (a) require no action by or in respect of, or filing with, any governmental body, agency or official and (b) do not contravene, or constitute a default under, any provision of applicable law or regulation or any judgment, injunction, order or decree or any agreement or other instrument binding upon the Company.

This opinion letter is provided to you for your use solely for the benefit of the Company in connection with the matters addressed herein and may not be used, circulated, quoted, or otherwise referred to or relied upon by any other person or for any other purpose without our express written consent or used in any other transaction or context. The only opinions rendered by us in this opinion letter consist of those matters set forth in numbered paragraphs (1) – (7) hereof, and no opinion may be implied or inferred beyond those opinions expressly stated herein. This opinion letter is rendered as of the date hereof and we make no undertaking, and expressly disclaim any duty, to supplement or update this opinion letter, if, after the date hereof, facts or circumstances come to our attention or changes in the law occur which could affect such opinion.

Insofar as the foregoing opinions relate to the legality, validity or binding effect of any agreement or obligation of the Company, such opinions are subject to subject to and limited by (i) the effects of general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law), including, without limitation, (a) principles governing the availability of specific performance, injunctive relief, or other equitable remedies, (b) principles affording traditional equitable defenses (e.g., waiver, laches and estoppel), (c) good faith and fair dealing, (d) reasonableness, (e) materiality of breach, (f) impracticability or impossibility of performance, (g) the effect of obstruction or failure to perform or otherwise act in accordance with an agreement by any person, and (h) unconscionability, the application of which may, among other things, deny parties thereto certain of the rights and remedies granted to them under

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the Securities or the Indenture, including, without limitation, rights to specific performance, injunctive relief, and the appointment of a receiver; (ii) the effect of bankruptcy, insolvency, fraudulent transfer, liquidation, reorganization, moratorium, conservatorship, receivership, or other similar laws of general applicability affecting the rights and remedies of creditors generally; and (iii) certain other limitations that exist relating to the rights of set-off, reimbursement (including, without limitation, for attorney’s fees and other expenses), indemnification, exculpation, or contribution by virtue of public policy.

We consent to the filing of this opinion as an exhibit to the Registration Statement. In giving our consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very Truly Yours,

        /S/ ALSTON & BIRD LLP