For sure. You have 2 22A 12V rails. Each rail will support 264Watts. My GTX 580s each use this much power at max load. If you were going with a GTX 580, I'd tell you to get something more for sure because you would regularly hit the limit.
Your 5770 will require around 8-10A from one of the rails at full load:http://www.guru3d.com/article/radeon-hd-5770-review-test/11
The system in the review shows a dual-5770 system running crossfire at 423Watts. Now I wouldn't advise you to get two 5770s unless you got a 650W or above (again my conservative side stepping in), but with that supply and a single 5770 you'll be fine.
You're working with an 80-plus rated PSU that is made to support moderate loads on its 12V rails. It is from a good reputable manufacturer.