You'd benefit from the 5850, but I doubt you'd benefit $300 worth.
5770 would be a sideways move: about the same in performance, with the added advantage of supporting DX11 -- which isn't a really big deal yet, though.
Honestly, I think you'd be better off waiting a few months and then seeing where prices are for the top cards then. The 4870 is still one of the better cards on the market in terms of performance. I wouldn't bother upgrading it unless the time comes when you either NEED DirectX11 for something, or you can get a card in the 5870-and-above performance range for less than $300, which obviously isn't possible yet.
Also, keep in mind that without knowing the specs of the rest of your system, this is only an educated guess. If you've got an old CPU and it's the weak link of the system, you could put in any video card you want and not notice much improvement.