I think 5,000 rigs is a little/lot high.  I think there are about 1,000 "rigs" in the GOM, but I don't know what the split is between drilling "rigs" and production "platforms" is - any help?
I stand corrected - CNN "more than 4,000 floating rigs and surrounding production platforms dot the GOM".  It appears that a rig can have some platforms floating in close proximity... these don't seem to manned, though...