Exhibit 10.5

ALLONGE TO SECURED PROMISSORY NOTE

(TRANCHE 2 ADVANCE)

This Allonge amends, and is affixed to, the Secured Promissory Note (Tranche 2 Advance), dated March 25, 2011, in the original principal amount of Ten Million Dollars ($10,000,000.00) made by Omeros Corporation to the order of Oxford Finance LLC (successor in interest to Oxford Finance Corporation) and attached hereto as Exhibit 1 (the “Note”). The Note was subsequently assigned to and is presently held by Oxford Finance Funding Trust 2012-01 (“Holder”).

The Note hereby is amended as follows:

The second paragraph of the Note hereby is amended and restated in its entirety to read as follows:

“On the Maturity Date (or upon earlier repayment, whether as a result of acceleration or otherwise) the Final Payment and the Prepayment Fee, as applicable (each as defined in and subject to the terms and conditions of the Loan Agreement) shall be due and payable by Borrower to Lender.”

The foregoing amendment shall have the same force and effect as though it were written directly into the Note. The Holder is hereby is instructed to attach this Allonge to the Note.

Dated: December 28, 2012

Exhibit 1

SECURED PROMISSORY NOTE

(TRANCHE 2 ADVANCE)

FOR VALUE RECEIVED, the undersigned, OMEROS CORPORATION, a Washington corporation (“Borrower”), HEREBY PROMISES TO PAY to the order of OXFORD FINANCE CORPORATION (“Lender”) the principal amount of Ten Million Dollars ($10,000,000) or such lesser amount as shall equal the outstanding principal balance of the Growth Capital Advance made to Borrower by Lender pursuant to the Loan Agreement (defined below), and to pay all other amounts due with respect to the Growth Capital Advance on the dates and in the amounts set forth in the Loan Agreement. Capitalized terms, unless defined in this Secured Promissory Note (this “Note”), shall have the meaning given such capitalized term in the Loan Agreement.

Interest on the principal amount of this Note from the date of this Note shall accrue at 8.558% per annum based on a 360-day year of twelve 30-day months or, if applicable, the Default Rate. Commencing on November 1, 2011, and continuing on the first day of each successive calendar month thereafter, Borrower shall make to Lender thirty-six (36) equal payments of principal and accrued interest on the then outstanding principal amount. Any and all remaining principal and interest shall be due and payable on the Maturity Date. In addition to the foregoing payments, on the Maturity Date (or upon earlier repayment, whether as a result of acceleration or otherwise) the Final Payment and the Prepayment Fee, as applicable (each as defined in and subject to the terms and conditions of the Loan Agreement) shall be due and payable by Borrower to Lender.

Principal, interest and all other amounts due with respect to the Growth Capital Advance, are payable in lawful money of the United States of America to Lender as set forth in the Loan Agreement. The principal amount of this Note and the interest rate applicable thereto, and all payments made with respect thereto, shall be recorded by Lender and, prior to any transfer hereof, endorsed on the grid attached hereto which is part of this Note.

This Note is the Note referred to in, and is entitled to the benefits of, the Loan and Security Agreement, dated as of October 21, 2010, to which Borrower and Lender are parties (as amended from time to time, the “Loan Agreement”). The Loan Agreement, among other things, (a) provides for the making of this secured Growth Capital Advance to Borrower, and (b) contains provisions for acceleration of the maturity hereof upon the happening of certain stated events.

This Note may not be prepaid except as provided in the Loan Agreement. This Note and the obligation of Borrower to repay the unpaid principal amount of the Growth Capital Advance, interest on the Growth Capital Advance and all other amounts due Lender under the Loan Agreement is secured under the Loan Agreement.

Presentment for payment, demand, notice of protest and all other demands and notices of any kind in connection with the execution, delivery, performance and enforcement of this Note are hereby waived.

Borrower shall pay all reasonable fees and expenses, including, without limitation, reasonable attorneys’ fees and costs, incurred by Lender in the enforcement or attempt to enforce any of Borrower’s obligations hereunder not performed when due. This Note shall be governed by, and construed and interpreted in accordance with, the laws of the State of California.

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IN WITNESS WHEREOF, the parties hereto have caused this Note to be executed as of the first date above written.