Exhibit 10.5

IDERA PHARMACEUTICALS, INC.

AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT

This Amendment No. 1 to Common Stock Purchase Warrant (this “Agreement”) is made
as of November 9, 2012, by and between Idera Pharmaceuticals, Inc., a Delaware
corporation (the “Company”), and Pillar Pharmaceuticals I, L.P. (the “Registered
Holder”).

WHEREAS, the Company issued and sold to the Registered Holder that certain
Common Stock Purchase Warrant, dated as of November 4, 2011 (the “Warrant”)
pursuant to that certain Convertible Preferred Stock and Warrant Purchase
Agreement, dated November 4, 2011, among the Company and the Purchasers named
therein;

WHEREAS, the Company and the Registered Holder desire to amend certain sections
of the Warrant, as set forth below;

WHEREAS, pursuant to Section 11 of the Warrant, any amendment of the Warrant
requires the written consent signed by the Company and the Registered Holder;

NOW, THEREFORE, in consideration of the foregoing, and for other valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, the
Company and the Registered Holder hereby agree as follows:

1. Section 1(e) of the Warrant is hereby amended by deleting subsection
(e) thereof in its entirety and inserting the following new subsection (e) in
lieu thereof:

“(e) Exercise Limitation. Notwithstanding anything to the contrary contained
herein, the Company shall not effect any exercise of this Warrant and the
Registered Holder shall not be entitled to exercise this Warrant for a number of
Warrant Shares in excess of that number of Warrant Shares which, upon giving
effect to such exercise, would cause (i) the aggregate number of shares of
Common Stock beneficially owned by the Registered Holder and its affiliates and
any other persons whose beneficial ownership of Common Stock would be aggregated
with the Registered Holder’s for purposes of Section 13(d) of the Securities
Exchange Act of 1934, as amended (the “Exchange Act”), to exceed 19.99% of the
total number of issued and outstanding shares of Common Stock of the Company
following such exercise, or (ii) the combined voting power of the securities of
the Company beneficially owned by the Registered Holder and its affiliates and
any other persons whose beneficial ownership of Common Stock would be aggregated
with the holder’s for purposes of Section 13(d) of the Exchange Act to exceed
19.99% of the combined voting power of all of the securities of the Company then
outstanding following such exercise, unless, in either case, the stockholders of
the Company approve the Nasdaq Proposal (as defined by and in accordance with
Section 5.11(B) of that certain Convertible Preferred Stock and Warrant, dated
November 9, 2012, among the Company and the Purchasers named therein), in which
case, the 19.99% limitation under clause (i) and clause (ii) of this
Section 1(e) shall be increased, with respect to the Registered Holder, to 35%
for purposes of both clause (i) and clause (ii) of this Section 1(e). For
purposes of this Section 1(e), the aggregate number of shares of Common Stock or
voting securities beneficially owned by the Registered Holder and its affiliates
and any other persons whose beneficial ownership of Common Stock would be
aggregated with the Registered Holder’s for purposes of Section 13(d) of the
Exchange Act shall include the shares of Common Stock issuable upon the exercise
of this Warrant with respect to which such determination is being made, but
shall exclude the number of shares of Common Stock which would be issuable upon
(i) exercise of the remaining unexercised and non-cancelled portion of this
Warrant by the Registered Holder and (ii) exercise or conversion of the
unexercised, non-converted or non-cancelled portion of any other securities of
the Company that do not have voting power (including without limitation any
securities of the Company which would entitle the holder thereof to acquire at
any time Common Stock, including without limitation any debt, preferred stock,
right, option, warrant or other instrument that is at any time convertible into
or exercisable or exchangeable for, or otherwise entitles the holder thereof to
receive, Common Stock), subject to a limitation on conversion or exercise
analogous to the limitation contained herein beneficially owned by the
Registered Holder or any of its affiliates and other persons whose beneficial
ownership of Common Stock would be aggregated with the Registered Holder’s for
purposes of Section 13(d) of the Exchange Act.”

--------------------------------------------------------------------------------

2. Section 13 of the Warrant is hereby amended by deleting the phrase
“Commonwealth of Massachusetts” and inserting the phrase “State of Delaware” in
lieu thereof.

3. The Warrant, as amended by this Agreement, together with any other writings
referred to in the Warrant or delivered pursuant thereto which form a part
thereof, contain the entire agreement among the parties with respect to the
subject matter thereof and amend, restate and supersede all prior and
contemporaneous arrangements or understandings with respect thereto.

4. Upon the effectiveness of this Agreement, on and after the date hereof, each
reference in the Warrant to “this Agreement,” “hereunder,” “hereof,” “herein” or
words of like import shall mean and be a reference to the Warrant, as amended
hereby. Except as specifically amended above, the Warrant shall remain in full
force and effect and are hereby ratified and confirmed.

5. This Agreement shall be governed by and construed in accordance with the
General Corporation Law of the State of Delaware as to matters within the scope
thereof, and as to all other matters shall be governed by and construed in
accordance with the internal laws of the State of Delaware, without regard to
conflict of laws principles that would result in the application of any law
other than the law of the State of Delaware.

6. This Agreement may be executed in any number of counterparts, and each such
counterpart shall be deemed to be an original instrument, but all such
counterparts together shall constitute but one agreement.

[Remainder of Page Intentionally Left Blank]

 

- 2 -

--------------------------------------------------------------------------------

IN WITNESS WHEREOF, this Amendment No. 1 to Common Stock Purchase Warrant has
been executed by the parties hereto as of the day and year first above written.

 

IDERA PHARMACEUTICALS, INC. By:   /s/ Sudhir Agrawal Name:   Sudhir Agrawal
Title:   Chairman, Chief Executive Officer and President

Amendment No. 1 to Common Stock Purchase Warrant

--------------------------------------------------------------------------------

IN WITNESS WHEREOF, this Amendment No. 1 to Common Stock Purchase Warrant has
been executed by the parties hereto as of the day and year first above written.

 

REGISTERED HOLDER: PILLAR PHARMACEUTICALS I, L.P. By:   /s/ Youssef El Zein
Name:   Youssef El Zein Title:   Director

Amendment No. 1 to Common Stock Purchase Warrant