I use the same rez and I have just done that move.
The HD5770 is a great improvement but I agree with Maziar: If you can afford it, go for the HD5850 instead, I do not play any super demanding games so the 5770 is fine, but you may find the extra power of a 5850 more useful than me.
Buy the new games and wait a while, Nvidia has yet to release its own next gen cards and once the 58xx become more available prices will most certainly drop.