Exhibit 5.1

Twist Bioscience Corporation

681 Gateway Blvd.

South San Francisco, CA 94080

Registration Statement on Form S-3 (No. 333-238906); 334,932 shares of common stock

Ladies and Gentlemen:

At your request, we have examined the Prospectus Supplement (as defined below), filed with the Securities and Exchange Commission (the “Commission”) relating to the offering from time to time, pursuant to Rule 415 of the General Rules and Regulations of the Commission promulgated under the Securities Act of 1933 (the “Securities Act”), by the selling stockholders named in the Prospectus Supplement (the “Selling Securityholders”), of 334,932 shares of common stock, par value $0.0001 per share (the “Shares”) of Twist Bioscience Corporation, a Delaware Corporation (the “Company”). The resale of the Shares is being registered pursuant to a registration statement on Form S-3 under the Securities Act, filed with the Commission on June 3, 2020 (Registration No. 333-238906) (the “Registration Statement”), a base prospectus dated June 3, 2020 included in the Registration Statement at the time it originally became effective (the “Base Prospectus”), and a prospectus supplement dated June 30, 2021 filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement,” and together with the Base Prospectus, the “Prospectus”).

We have examined the originals, or copies identified to our satisfaction, of such corporate records of the Company, certificates of public officials, officers of the Company, and other persons, and such other documents, agreements and instruments as we have deemed relevant and necessary for the basis of our opinions hereinafter expressed. In such examination, we have assumed the following: (a) the authenticity of original documents and the genuineness of all signatures; (b) the conformity to the originals of all documents submitted to us as copies; and (c) the truth, accuracy, and completeness of the information, representations, and warranties contained in the records, documents, instruments, and certificates we have reviewed.

June 30, 2021

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Based on and subject to the foregoing, we are of the opinion that the Shares have been duly authorized and are validly issued, fully paid and nonassessable.

We express no opinion as to laws other than the laws of the State of Delaware with respect to the opinion set forth above, and we express no opinion with respect to the applicability thereto, or the effect thereon, of any other laws, or as to any matters of municipal law or the laws of any local agencies within any state.

We hereby consent to the reference to us under the heading “Legal Matters” in the Prospectus and to the filing of this opinion as Exhibit 5.1 to the Registration Statement. By giving this consent, we do not 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 promulgated thereunder.

Very truly yours,

/s/ Orrick, Herrington & Sutcliffe LLP

ORRICK, HERRINGTON & SUTCLIFFE LLP