I did T5 to T3 the other day as well, granted it was maybe 6:10am but it was easy as pie. Bus arrived in 2-3 minutes, plenty of room, FastTrack security at T3 FCC wasn't open but there was virtually no line.

I was initially quite annoyed as my AA-BA connection was originally T3-T3, but due to a shocking 2 hour delay on AA (delayed inbound due to 77W maintenance), I switched to BA-BA that required the terminal change (and got me stuck in a horrid middle seat in J, but that's another story).