FIRST AMENDMENT TO THE INFONXX, INC. SECOND AMENDED AND RESTATED 1996 STOCK PLAN

EXHIBIT 10.5

FIRST AMENDMENT

TO THE

INFONXX, INC. SECOND AMENDED AND RESTATED 1996 STOCK PLAN

THIS FIRST AMENDMENT is made on the 20th day of January, 2005, by INFONXX, INC., a Delaware corporation (the “Company”).

WHEREAS, the Company maintains the INFONXX, Inc. Second Amended and Restated 1996 Stock Plan (the “Plan”); and

WHEREAS, the Company desires to amend the Plan definition of “Change in Control” to exclude certain acquisitions of shares of the Company’s capital stock, directly or indirectly, by Thomas J. Tisch and members of his family;

NOW, THEREFORE, BE IT RESOLVED, that, effective for all options granted under the Plan on or after January 1, 2005, and any outstanding option agreements under the Plan which are amended on or after January 1, 2005 (to the extent the amended option agreement so allows), the Company does hereby amend the Plan as follows:

1. By deleting the existing Section 2(d)(i) and substituting in lieu thereof the following:

“(i) When any ‘person,’ as such term is used in Section 13(d) and 14(d) of the Exchange Act (other than the Company, a Subsidiary, one or more members of the Tisch Group acting individually or jointly, or a Company employee benefit plan, including any trustee of such plan acting as trustee) is or becomes the ‘beneficial owner’ (as defined in Rule 13d-3 under the Exchange Act), directly or indirectly, of securities of the Company representing more than fifty percent (50%) of the combined voting power of the Company’s then outstanding securities entitled to vote generally in the election of directors;”

2. By adding the following new Section 2(ee):

“(ee) ‘Tisch Group’ means:

(i) Thomas J. Tisch, the spouse of Thomas J. Tisch, a lineal ascendant or descendant of Thomas J. Tisch or the spouse of a lineal ascendant or descendant of Thomas J. Tisch, the brother or sister of Thomas J. Tisch, and a lineal descendant of the brother or sister of Thomas J. Tisch (the ‘Tisch Family Members’);

(ii) any entity controlled directly or indirectly by one or more individuals who are Tisch Family Members, individually or jointly; and

(iii) any trust as to which one or more Tisch Family Members, individually or jointly, is a grantor or has a beneficial interest.

The Tisch Group includes, but is not limited to, Thomas J. Tisch, The Andrew H. Tisch 1995 Issue Trust No. 1, The Andrew H. Tisch 1995 Issue Trust No. 2, The Daniel R. Tisch 1991 Trust, The James S. Tisch 1995 Issue Trust, The Thomas J. Tisch 1994 Issue Trust, Andrew H. Tisch 2002 Annuity Trust V, Daniel R. Tisch 2002 Annuity Trust V, James S. Tisch 2002 Annuity Trust V, The Andrew H. Tisch 2003 Annuity Trust VI, The Daniel R. Tisch 2003 Annuity Trust VI, The James S. Tisch 2003 Annuity Trust VI, The Thomas J. Tisch 2003 Annuity Trust VII, and The Thomas J. Tisch 8/16/04 Annuity Trust.”

Except as specifically amended hereby, the remaining provisions of the Plan shall remain in full force and effect as prior to the adoption of this First Amendment.

IN WITNESS WHEREOF, the Company has caused this First Amendment to be executed, on the date first above written.