That sounds a bit fishy, 5770 shouldn't have enough power for maxed Crysis. So I went and looked it up and, sure enough:
http://www.anandtech.com/video/showdoc.aspx?i=3658&p=5
http://i416.photobucket.com/albums/p...anbg/20444.png
And it only gets worse on higher resolutions. I'd say turn AA off, lower shader settings by a bit and play on lower resolutions. If it's still unplayable, you might be bottlenecked somewhere else (like, say, your processor). And of course, as you mention, having latest drivers for everything is always important.