I believe BFG made 2 450w PSU's, one is 29A on a single rail, the other (2) 18A rails totallying about 25A. So I would feel a 5770 is very comfortable on that setup. A 5850 actually consumes slightly less power than a 4870, and you might be ok with it on your system, but my comfort level wouldn't be at the 100% mark.
I like BFG PSU's and they have made several that I think I'd select even over a Corsair (not a die hard fan of Corsair. I dunno why people get gaga over them, they are good but not the crown royal of the crew)