Judging from Peter Davis' Facebook Status:

Peter Davis: can't accept more friend requests. FB has capped me at 5001. It's like winning a video game, only to really lose big time. I have complained to FB!!
Updated 2 hours ago

It really is possible to be too popular.  And, according to Facebook's standards, 5001 is the magic number before you get there.  I can't tell you how glad I am that I got in as Peter's friend before he hit this mark!