Exhibit 5.1

May 16, 2012

Texas Capital Bancshares, Inc.

2000 McKinney Avenue, Suite 700

Dallas, Texas 75201

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Texas Capital Bancshares, Inc., a Delaware corporation (the “Corporation”), in connection with a Registration Statement on Form S-3 (the “Registration Statement”) filed by the Corporation with the Securities and Exchange Commission (“the Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration and proposed issuance and sale from time to time pursuant to Rule 415 under the Securities Act of $250,000,000 aggregate principal amount of (the “Registered Securities”): (i) the Corporation’s unsecured debt securities, whether senior or subordinated (the “Debt Securities”); (ii) shares of common stock, $0.01 par value per share, of the Corporation (the “Common Stock”); (iii) shares of preferred stock, $0.01 par value per share, of the Corporation (the “Preferred Stock”); (iv) warrants to purchase Common Stock (the “Warrants”); and (v) the Corporation’s units comprised of two or more of the Registered Securities in any combination (the “Units”).

Each series of Debt Securities will be issued pursuant to a Senior Debt Securities Indenture (as amended or supplemented from time to time, the “Senior Debt Indenture”) or a Subordinated Debt Securities Indenture (as amended or supplemented from time to time the “Subordinated Debt Indenture”), as applicable, the forms of which have been filed as exhibits to the Corporation’s Registration Statement on Form S-3 filed with the Commission on April 15, 2009 (collectively, the “Indentures”) and are to be entered into, in each case, between the Corporation and a trustee (the “Trustee”). The Debt Securities are to be issued in the forms set forth in the Indentures.

We have examined originals or copies certified or otherwise identified to our satisfaction of the following:

(i) The Corporation’s Certificate of Incorporation, as amended, as in effect on the date hereof.

(ii) The Corporation’s Amended and Restated Bylaws, as in effect on the date hereof.

(iii) Certain resolutions duly adopted by the Board of Directors of the Corporation related to the offering of the Registered Securities and related matters.

(iv) The Registration Statement and exhibits thereto, including the Indentures and the forms of Registered Securities.

(v) Such other instruments, documents and records as we have deemed necessary and relevant for the purposes hereof.

In the course of our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified or photostatic copies and the authenticity of the originals of such latter documents. In making our examination of documents executed by parties other than the Corporation, we have assumed that such parties had the power,

corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and execution and delivery by such parties of such documents and the validity, binding effect and enforceability thereof on such parties.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that:

1. When, as and if (a) the appropriate corporate action has been taken by the Corporation to authorize the form, terms, execution and delivery of any series of Debt Securities, (b) such Debt Securities shall have been issued in the form and containing the terms set forth in the Registration Statement, the applicable Indenture and such corporate action, (c) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities are obtained, and (d) the Debt Securities have been authenticated by the Trustee, then, upon the happening of such events, such Debt Securities will constitute valid and binding obligations of the Corporation, enforceable against the Corporation in accordance with their terms.

2. When, as and if (a) appropriate corporate action has been taken to authorize the issuance of Common Stock, (b) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities are obtained, (c) Common Stock shall have been duly issued and delivered by the Corporation against payment therefor in accordance with such corporate action, and (d) certificates representing shares of Common Stock have been duly executed by the duly authorized officers of the Corporation in accordance with applicable law, then, upon the happening of such events, such Common Stock will be validly issued, fully paid and non-assessable (provided that the consideration paid therefor is not less than the par value thereof).

3. When, as and if (a) appropriate corporate action has been taken to authorize the issuance of Preferred Stock, to fix the terms thereof and to authorize the execution and filing of a certificate of designation relating thereto with the Secretary of State of the State of Delaware, (b) such certificate of designation shall have been executed by duly authorized officers of the Corporation and so filed by the Corporation, all in accordance with the laws of the State of Delaware, (c) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities are obtained, (d) Preferred Stock with terms so fixed shall have been duly issued and delivered by the Corporation against payment therefor in accordance with such corporate action, and (e) certificates representing shares of Preferred Stock have been duly executed by the duly authorized officers of the Corporation in accordance with applicable law, then, upon the happening of such events, such Preferred Stock will be validly issued, fully paid and non-assessable (provided that the consideration paid therefor is not less than the par value thereof).

4. When, as and if (a) the appropriate corporate action has been taken by the Corporation to authorize the form, terms, execution and delivery of a warrant agreement (including a form of certificate evidencing the Warrants) (a “Warrant Agreement”), (b) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities are obtained, and (c) Warrants with such terms are duly executed, attested, issued and delivered by duly authorized officers of the Corporation against payment in the manner provided for in the applicable Warrant Agreement and such corporate action, then, upon the happening of such events, such Warrants will constitute valid and binding obligations of the Corporation, enforceable against the Corporation in accordance with their terms.

5. When, as and if (a) the appropriate corporate action has been taken by the Corporation to authorize the form, terms, execution and delivery of a unit agreement relating to Units (including a form of certificate evidencing the Units) (a “Unit Agreement”) (b) any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities are obtained, and (c) the Units

with such terms are duly executed, attested, issued and delivered by duly authorized officers of the Corporation against payment in the manner provided for in the Unit Agreement and such corporate action, then, upon the happening of such events, such Units will constitute valid and binding obligations of the Corporation, enforceable against the Corporation in accordance with their terms.

Our opinions set forth above are subject to the effects of (i) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally, (ii) general equitable principles (whether considered in a proceeding in equity or at law), (iii) an implied covenant of good faith and fair dealing and (iv) limitation of rights to indemnification, exculpation and contribution which may be limited by applicable law or equitable principles. We express no opinion regarding the effectiveness of any waiver of stay, extension or usury laws or of unknown future rights, and we express no opinion regarding severability provisions.

The opinion letter which we render herein is limited to those matters governed by the laws of the State of Delaware, the relevant contract law of the State of New York and the federal laws of the United States as of the date hereof. Our opinions expressed herein are as of the date hereof, and we assume no obligation to revise or supplement the opinions rendered herein should the above-referenced laws be changed by legislative or regulatory action, judicial decision or otherwise. We express no opinion as to compliance with the “blue sky” laws of any jurisdiction and the opinions set forth herein are qualified in that respect.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the references to us under the heading “Legal Matters” in the prospectus forming part of the Registration Statement and any supplement thereto. In giving such consent, we do not thereby 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 promulgated thereunder.

Very truly yours,

/s/ Winstead PC

Winstead PC