The answer is nobody. There is no NFL games that time of year. If the question was maybe week 13 in 2007 then it was the Green Bay Packers, or if it was Sunday January 13 2007 it would be New York Giants.
Sunday May 13th was in 2007.
May 20, 2007 fell on a Sunday.
Since this answer may be read months or years from now, the best answer is to send you the the link, below, where you will find the Cowboys' schedule.
Sunday
Sunday Best - 2007 - 2.10 was released on: USA: 10 May 2009
Sunday Best - 2007 2-10 was released on: USA: 10 May 2009
Mother's Day 2007 was celebrated on Sunday May 13.
Sunday Night Heat - 1998 2007-05-04 was released on: USA: 4 May 2007
Sunday Night Heat - 1998 2007-05-11 was released on: USA: 11 May 2007
Sunday Night Heat - 1998 2007-05-18 was released on: USA: 18 May 2007
Sunday Night Heat - 1998 2007-05-25 was released on: USA: 25 May 2007
The U.K. Singles Chart week runs from Sunday to Sunday. The number one single for the week of May 6, 2007 was "Beautiful Liar" by Beyonce featuring Shakira. The number one single for the week of May 13, 2007 was "Baby's Coming Back/Transylvania" by McFly.