Twist Bioscience (TWST) 8-K Entry into a Material Definitive Agreement

Exhibit 5.1

Orrick, Herrington & Sutcliffe LLP

The Orrick Building

405 Howard Street

San Francisco, CA 94105-2669

+1-415-773-5700

orrick.com

June 5, 2020

Twist Bioscience Corporation

681 Gateway Blvd.

South San Francisco, CA 94080

Re: 3,484,848 Shares of Common Stock of Twist Bioscience Corporation

Ladies and Gentlemen:

We have acted as counsel for Twist Bioscience Corporation, a Delaware corporation (the “Company”), in connection with the offering by the Company of 3,484,848 shares of the Company’s common stock, par value $0.00001 per share (the “Shares”), including 454,545 Shares purchasable by the underwriters upon their exercise of the option granted to the underwriters by the Company to purchase additional shares, pursuant to an automatic shelf registration statement on FormS-3 (Registration StatementNo. 333-238906) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), including the prospectus dated June 3, 2020 included therein (the “Base Prospectus”), and the prospectus supplement dated June 3, 2020, filed with the Commission pursuant to Rule 424(b) of the rules and regulations of the Act (the “Prospectus Supplement”). The Base Prospectus and the Prospectus Supplement are collectively referred to as the “Prospectus.” The Shares are to be sold by the Company in the manner described in the Registration Statement and the Prospectus.

In connection with rendering this opinion, we have examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of (i) the Amended and Restated Certificate of Incorporation of the Company, as amended through the date hereof, (ii) the Amended and Restated Bylaws of the Company, as amended through the date hereof, (iii) certain resolutions of the Board of Directors of the Company and its Special Finance Committee relating to the issuance, sale and registration of the Shares, (iv) the Registration Statement, (v) the Prospectus, and (vi) such corporate records, agreements, documents and other instruments, and such certificates or comparable documents of public officials and of officers and representatives of the Company, and have made such inquiries of such officers and representatives, as we have deemed relevant and necessary or appropriate as a basis for the opinion set forth below.

June 5, 2020

Page 2

In 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 facsimile, electronic, certified or photostatic copies, and the authenticity of the originals of such copies. In making our examination of documents executed or to be executed, we have assumed that the parties thereto, other than the Company, had or will have 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 the execution and delivery by such parties of such documents and the validity and binding effect thereof on such parties. As to any facts material to the opinions expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

Based on the foregoing and subject to the limitations, qualifications and assumptions set forth herein, we are of the opinion that the Shares have been duly authorized and, upon issuance, delivery and payment therefor in the manner contemplated by the Registration Statement and the Prospectus, will be validly issued, fully paid andnon-assessable.

The opinion expressed herein is limited to the General Corporation Law of the State of Delaware and the federal laws of the United States of America, and we express no opinion as to the effect on the matters covered by this letter of the laws of any other jurisdictions.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and the reference to us under the caption “Legal matters” in the Prospectus. In giving such consent, we do not hereby admit that we are included in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ ORRICK, HERRINGTON & SUTCLIFFE LLP

ORRICK, HERRINGTON & SUTCLIFFE LLP