I imagine part of it was not wanting to give the ball back to Peyton and figuring if they didn't convert they wouldn't lose that much net yardage (obviously that didn't work out), but Reiss offers another possible explanation:
"Some took issue with Bill Belichick's decision to go for it on fourth-and-5 with 8:17 remaining in the game, the ball on the Broncos' 37, and the Patriots leading 31-14. CBS analyst Phil Simms was among those questioning the move. It's a good debate. I think Belichick went for it, in part, because of the left foot injury that previously knocked Tracy White out of the game and how that affected the punt team. White is the left wing on the punt team, and on the previous punt, the Broncos were close to a block as White's replacement, Nate Ebner, was penalized for holding. Ebner's struggles in punt protection are there for everyone to see on film (blocked punt in Week 2 vs. Cardinals) and my sense is that Belichick was thinking, "Why chance it?" Hard to argue with that line of thinking given the position on the field and the yardage needed, even though the results in going for it were disastrous."
Interesting analysis. Full link here (http://espn.go.com/blog/boston/new-england-patriots/post/_/id/4731800/closing-the-book-on-pats-broncos)