Exhibit 5.1

  SIDLEY AUSTIN LLP 2021 MCKINNEY AVENUE SUITE 2000 DALLAS, TX 75201 +1 214 981 3300 +1 214 981 3400 FAX   AMERICA   •   ASIA PACIFIC   •   EUROPE

January 23, 2024

Vistra Corp.

6555 Sierra Dr.,

Irving, TX 75039

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We refer to the Registration Statement on Form S-3 (the “Registration Statement”) being filed by Vistra Corp., a Delaware corporation (the “Company”), with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the resale from time to time by certain selling stockholders of an aggregate of up to 476,081.109 shares of Vistra Corp. 8.875% Series C Fixed-Rate Reset Cumulative Redeemable Perpetual Preferred Stock (the “Series C Preferred Shares”).

This opinion letter is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

We have examined the Registration Statement, the exhibits thereto (including the Certificate of Designation filed with the Secretary of State of Delaware on December 20, 2023), the certificate of incorporation of the Company, as amended to the date hereof, and the bylaws of the Company, as amended to the date hereof, and the resolutions adopted by the board of directors of the Company relating to the Registration Statement. We have also examined originals, or copies of originals certified to our satisfaction, of such agreements, documents, certificates and other documents of the Company and others, and have examined such questions of law, as we have considered relevant and necessary as a basis for this opinion letter. We have assumed the authenticity of all documents submitted to us as originals, the genuineness of all signatures, the legal capacity of all persons and the conformity with the original documents of any copies thereof submitted to us for examination. As to facts relevant to the opinion expressed herein, we have relied, without independent investigation or verification, upon, and assumed the accuracy and completeness of, certificates, letters and oral and written statements and representations of officers and other representatives of the Company.

Based on, and subject to, the foregoing and the other limitations, qualifications and assumptions set forth herein, we are of the opinion that the Series C Preferred Shares are validly issued, fully paid and nonassessable.

This opinion letter is limited to the General Corporation Law of the State of Delaware. We express no opinion as to the laws, rules or regulations of any other jurisdiction, including, without limitation, the federal laws of the United States of America or any state securities or blue sky laws.

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We hereby consent to the filing of this opinion letter as an Exhibit to the Registration Statement and to all references to our firm included in or made a part of the Registration Statement. 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.

Very truly yours,

/s/ Sidley Austin LLP