Exhibit (a)(5)(E)

[FORM OF SUMMARY ADVERTISEMENT]

This announcement is neither an offer to purchase nor a solicitation of an offer to sell securities. The Offer (as defined below) is made solely pursuant to the Offer to Purchase (as defined below), and the related Letter of Transmittal (as defined below), and is being made to all holders of Shares (as defined below). Cubist (as defined below) and Purchaser (as defined below) are not aware of any jurisdiction where the making of the Offer is prohibited by any administrative or judicial action pursuant to any valid statute of any jurisdiction. If Cubist and Purchaser become aware of any valid statute of any jurisdiction prohibiting the making of the Offer or the acceptance of the Shares, Cubist and Purchaser will make a good faith effort to comply with such statute. If, after a good faith effort, Cubist and Purchaser cannot comply with the statute of the jurisdiction, Cubist and Purchaser will not make the Offer to, nor accept for payment Shares tendered by or on behalf of, Trius’ (as defined below) stockholders in that jurisdiction.

Notice of Offer to Purchase

All Outstanding Shares of Common Stock

Trius Therapeutics, Inc.

BRGO Corporation

a wholly-owned subsidiary of

Cubist Pharmaceuticals, Inc.

$13.50 Per Share in Cash

plus

Up to $2.00 Per Share in Contingent Cash Payments

Cubist Pharmaceuticals, Inc. (“Cubist”), through its wholly-owned subsidiary, BRGO Corporation (“Purchaser”), is offering to purchase all of the outstanding shares of common stock, par value $0.0001 per share (the “Shares”), of Trius Therapeutics, Inc. (“Trius”), for consideration of (1) $13.50 per Share, in cash (the “Closing Amount”), plus (2) one non-transferable contingent value right (“CVR”) per Share, which represents the contractual right to receive up to an additional $2.00 in cash, if specified sales milestones are achieved within an agreed upon time period, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated August 13, 2013 (together with any amendments or supplements thereto, the “Offer to Purchase”), and in the related Letter of Transmittal (together with any amendments or supplements thereto, the “Letter of Transmittal” and, together with the Offer to Purchase, the “Offer”). The Closing Amount and any amounts paid with respect to CVRs will be subject to any required withholding of taxes, and no interest will be paid thereon. The CVRs will not be transferable, except under very limited circumstances as described in the Offer to Purchase, and will not have any voting or dividend rights or represent any equity interest in Cubist, Trius or Purchaser. Holders of record of Shares who tender their Shares directly to Purchaser in the Offer will not be obligated to pay brokerage fees or similar expenses or, except as otherwise provided in Instruction 6 of the Letter of Transmittal, stock transfer taxes with respect to the sale of Shares pursuant to the Offer. Stockholders who hold their Shares through a broker, dealer, commercial bank, trust company or other nominee should check with those institutions as to whether or not they charge any fee or commission.

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 9:00 A.M. EASTERN TIME ON WEDNESDAY, SEPTEMBER 11, 2013, UNLESS THE OFFER IS EXTENDED.

The Offer is conditioned upon, among other things, there being validly tendered and not properly withdrawn prior to the expiration of the Offer (as extended in accordance with the Merger Agreement (as defined below)) a number of Shares that, when considered together with all other Shares (if any) beneficially owned by Cubist and its affiliates, represents at least a majority of the total number of Shares outstanding on a fully-diluted basis (the “Minimum Condition”), and the applicable waiting periods under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended (the “HSR Act”) having expired or been terminated. The Offer is also subject to the other terms and conditions set forth in the Offer to Purchase. See Section 14—“Conditions of the Offer” of the Offer to Purchase.

The Offer is being made pursuant to an Agreement and Plan of Merger, dated as of July 30, 2013 (the “Merger Agreement”), among Cubist, Purchaser and Trius. The Merger Agreement provides that, after the

completion of the Offer and the satisfaction or waiver of the conditions to the Merger (as defined below), at the effective time of the Merger (the “Effective Time”), Purchaser will merge with and into Trius (the “Merger”). Following the Merger, Purchaser’s separate corporate existence will cease and Trius will continue as the surviving corporation and a wholly-owned subsidiary of Cubist. If Purchaser acquires at least 90% of the outstanding Shares, the parties have agreed, at the request of Cubist, to cause the Merger to become effective as soon as practicable after such acquisition, without a meeting of stockholders of Trius, in accordance with and subject to the General Corporation Law of the State of Delaware (the “DGCL”). At the Effective Time, by virtue of the Merger and without any action on the part of Trius, Purchaser, Cubist or any holder of Shares, each Share issued and outstanding immediately prior to the Effective Time (other than (1) any Shares held by Trius (or held in Trius’ treasury) or owned by Cubist, Purchaser or any subsidiary of Cubist and (2) any Shares held by a holder who has not voted in favor of or consented to the Merger and who has properly demanded and perfected his, her or its right to be paid the fair value of such Shares (“Appraisal Shares”) in accordance with the provisions of Section 262 of the DGCL) will be automatically canceled and converted into the right to receive the Closing Amount plus one CVR, or any such higher consideration as may be paid in the Offer (the “Merger Consideration”). If a holder of Appraisal Shares fails to validly perfect or loses such appraisal rights, then the Appraisal Shares held by such holder will be deemed to have been canceled at the Effective Time, and such holder will be entitled to receive only the Merger Consideration (payable without any interest thereon) in respect of his, her or its Shares. See Section 12 —“Purpose of the Offer; the Merger Agreement; Contingent Value Rights Agreement and CVRs; Tender and Voting Agreement; Confidentiality Agreement; Plans for Trius; Extraordinary Corporate Transactions; Appraisal Rights; Going-Private Transactions” of the Offer to Purchase.

The board of directors of Trius has (1) determined that the Merger Agreement and the Transactions (as defined in the Merger Agreement), including the Offer and the Merger, are advisable to, and in the best interest of, Trius and its stockholders, (2) approved the execution, delivery and performance by Trius of the Merger Agreement and the consummation of the Transactions, including the Offer and the Merger, (3) authorized and approved the Top-Up Option (as defined below) and the issuance of the Top-Up Shares (as defined below) and (4) resolved to recommend that the stockholders of Trius tender their Shares to Purchaser pursuant to the Offer, and, if applicable, approve the adoption of the Merger Agreement and the Merger.

For purposes of the Offer, Purchaser will be deemed to have accepted for payment, and purchased, Shares validly tendered and not properly withdrawn, if and when Purchaser gives oral or written notice to Computershare Trust Company, N.A., the depositary for the Offer (the “Depositary”), of Purchaser’s acceptance of the Shares for payment pursuant to the Offer. Purchaser’s acceptance for payment of Shares tendered in the Offer will constitute a binding agreement between Purchaser and each tendering stockholder. In all cases, upon the terms and subject to the conditions of the Offer, payment for Shares purchased pursuant to the Offer will be made by deposit of the Closing Amount for the Shares with the Depositary, which will act as agent for tendering Trius stockholders for the purpose of receiving the Closing Amount from Purchaser and transmitting the Closing Amount for Shares validly tendered and not properly withdrawn, and by the execution of the Contingent Value Rights Agreement (the “CVR Agreement”) by Cubist and Broadridge Corporate Issuer Solutions, Inc., as rights agent (the “Rights Agent”). In all cases, Purchaser has agreed to pay for Shares accepted for payment in the Offer only after timely receipt by the Depositary of (1) certificates representing the Shares (“Share Certificates”) or timely confirmation of the book-entry transfer of the Shares into the Depositary’s account at The Depository Trust Company (the “Book-Entry Transfer Facility”), pursuant to the procedures set forth in Section 2—“Procedures for Tendering Shares” of the Offer to Purchase, (2) the Letter of Transmittal or a facsimile thereof, properly completed and duly executed, with any required signature guarantees, or an Agent’s Message, as defined in the Offer to Purchase, in connection with a book-entry transfer, and (3) any other documents that the Letter of Transmittal requires. Any contingent cash payments will be made in accordance with the CVR Agreement that Cubist and the Rights Agent, will enter into at or prior to the acceptance of the Shares pursuant to the Offer. Purchaser and Cubist have included the form of CVR Agreement as exhibit (d)(2) to the Tender Offer Statement on Schedule TO filed by Purchaser and Cubist with the U.S. Securities and Exchange Commission. The CVRs will not be evidenced by any certificates.

If the conditions to the Offer have not been satisfied or waived and the Merger Agreement has not been terminated, (1) Purchaser may, without the consent of Trius, extend the Offer on one or more occasions until all conditions of the Offer have been satisfied or waived and (2) Trius may require Purchaser to extend the Offer until all conditions to the Offer have been satisfied or waived, provided that Trius may only request one extension of up to 10 business days if the Minimum Condition has not been satisfied. See Section 14—“Conditions of the Offer” of the Offer to Purchase. In addition,

Purchaser (1) may, without the consent of Trius, provide a subsequent offering period for the Offer in accordance with Rule 14d-11 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), following Purchaser’s acceptance for payment of Shares in the Offer and (2) will extend the Offer (a) for any period required by any legal requirement applicable to the Offer or (b) for periods of up to 10 business days per extension, until any waiting period related to the consummation of the Offer under the HSR Act has expired or been terminated.

In addition, Trius has granted Purchaser an irrevocable option (the “Top-Up Option”) to purchase, at a price per Share equal to the greater of (i) the last reported sale price of a Share on The NASDAQ Global Market on the last trading day prior to the date on which the Top-Up Option is exercised or (ii) the Closing Amount, that number of newly issued Shares sufficient to cause Purchaser to own at least 90% of the outstanding Shares entitled to vote on the Merger. The number of additional Shares that Purchaser can purchase under the Top-Up Option is limited to the number of authorized but unissued Shares at the time the Top-Up Option is exercised. Purchaser may exercise the Top-Up Option only if, among other things, the Minimum Condition is satisfied. See Section 12 —“Purpose of the Offer; the Merger Agreement; Contingent Value Rights Agreement and CVRs; Tender and Voting Agreement; Confidentiality Agreement; Plans for Trius; Extraordinary Corporate Transactions; Appraisal Rights; Going-Private Transactions” of the Offer to Purchase.

Any extension, delay, termination, waiver or amendment of the Offer will be followed promptly by public announcement. The announcement, in the case of an extension, will be made no later than 9:00 a.m. Eastern time on the next business day after the previously scheduled Expiration Date (as defined below), in accordance with the public announcement requirements of Rule 14e-1(d) under the Exchange Act. If Purchaser extends the Expiration Date, all Shares previously tendered and not properly withdrawn will remain subject to the Offer and subject to the tendering stockholder’s right to withdraw the stockholder’s Shares. “Expiration Date” means 9:00 a.m. Eastern time on Wednesday, September 11, 2013, unless the period during which the Offer is open is extended, in which event the term “Expiration Date” means the latest time and date at which the Offer, as so extended, expires.

Other than during a subsequent offering period, tendering stockholders may withdraw Shares that have been previously tendered in the Offer at any time on or prior to the Expiration Date (including any extension of such date and time), and, unless theretofor accepted for payment as provided in the Offer to Purchase, tendering stockholders may also withdraw such Shares at any time on or after October 12, 2013. No withdrawal rights apply to Shares tendered in a subsequent offering period, and no withdrawal rights apply during any subsequent offering period with respect to Shares tendered in the Offer and accepted for payment.

In order for a withdrawal to be proper and effective, the stockholder must deliver a written or facsimile transmission notice of withdrawal to the Depositary at one of its addresses or fax numbers set forth on the back cover of the Offer to Purchase. Any such notice of withdrawal must specify the stockholder’s name, the number of Shares that the stockholder wants to withdraw, and (if Share Certificates have been tendered) the name of the registered holder of Shares as shown on the Share Certificate, if different from the stockholder’s name. If Share Certificates have been delivered or otherwise identified to the Depositary, then, prior to the physical release of Share Certificates, the stockholder must submit the serial numbers shown on the particular Share Certificates evidencing Shares to be withdrawn and an Eligible Institution, as defined in the Offer to Purchase, must guarantee the signature on the notice of withdrawal, except in the case of Shares tendered for the account of an Eligible Institution. If Shares have been tendered pursuant to the procedures for book-entry transfer set forth in Section 2—“Procedures for Tendering Shares” of the Offer to Purchase, the notice of withdrawal must specify the name and number of the account at the Book-Entry Transfer Facility to be credited with the withdrawn Shares and must otherwise comply with the procedures of the Book-Entry Transfer Facility, in which case a notice of withdrawal will be effective and proper if delivered to the Depositary by any method of delivery described in the first sentence of this paragraph. Stockholders may not rescind a withdrawal of Shares. Any Shares that are properly withdrawn will not be considered as validly tendered for purposes of the Offer, but may be tendered again at any time before the Expiration Date by following the procedures described in Section 2—“Procedures for Tendering Shares” of the Offer to Purchase.

The information required to be disclosed by Rule 14d-6(d)(1) of the General Rules and Regulations under the Exchange Act is contained in the Offer to Purchase and is incorporated herein by reference.

Trius has provided Cubist and Purchaser with its stockholder list and security position listings for the purpose of disseminating the Offer to Trius’ stockholders. Purchaser will mail the Offer to Purchase, the related Letter of Transmittal and, if required, other relevant materials to record holders of Shares, and Purchaser will furnish the same materials to brokers, dealers, commercial banks, trust companies and similar persons whose names, or the names of whose nominees, appear on the stockholder list or, if applicable, that are listed as participants in a clearing agency’s security position listing, for forwarding to beneficial owners of Shares.

The receipt of cash and CVRs in exchange for Shares pursuant to the Offer or the Merger generally will be a taxable transaction for U.S. federal income tax purposes. The amount of gain or loss a holder recognizes, and the timing and character of such gain or loss, depends on the U.S. federal income tax treatment of the CVRs, with respect to which there is uncertainty. See Section 5— “Material United States Federal Income Tax Consequences” of the Offer to Purchase for a more detailed discussion of the tax treatment of the Offer. You are urged to consult with your own tax advisor as to the particular tax consequences to you of the Offer and the Merger.

The Offer to Purchase and the related Letter of Transmittal contain important information that Trius’ stockholders should read carefully and consider before making any decision with respect to the Offer.

Stockholders may direct questions and requests for assistance to the information agent at its address and telephone numbers set forth below. Stockholders may obtain copies of the Offer to Purchase, the related Letter of Transmittal and other tender offer materials from the information agent as set forth below, and they will be furnished promptly at Cubist’s expense. Stockholders also may contact their broker, dealer, commercial bank, trust company or other nominee for assistance concerning the Offer. Purchaser will pay all charges and expenses of Computershare Trust Company, N.A., as depositary for the Offer, and MacKenzie Partners, Inc., as information agent for the Offer, incurred in connection with the Offer. Cubist will reimburse brokers, dealers, commercial banks, trust companies and other nominees, upon request, for customary clerical and mailing expenses incurred by them in forwarding tender offer materials to their customers.

The Information Agent for the Offer is:

105 Madison Avenue

New York, New York 10016

(212) 929-5500 (Call Collect)

Call Toll-Free (800) 322-2885

Email: tenderoffer@mackenziepartners.com

August 13, 2013