I had really bad luck with the 5770 (mine was the newer model from Sapphire with the egg-shaped cooler). After two bad cards in a row, I got a refund and switched to a GTX 260.
The first 5770 worked fine for about a month then the screen went black in the middle of a game. After rebooting, the computer would not post and the BIOS screen had corrupted graphics. After several attempts, I got it to post but only got intermittent video (text mode seemed to work, but not graphics).
I RMAed that one and the replacement posted and showed video OK but the video driver crashed every time Windows 7 enabled or disabled Aero. For example, any time a UAC prompt appeared, or if I changed my theme manually.
The GTX 260 I replaced it with has been completely stable since I installed it two weeks ago.
Tom's reported a while back that a lot of people are having similar problems to the ones I had with my second card:
http://www.tomshardware.com/news/ATI-Radeon-Gray-Screen-Crash,9529.html?xtmc=ati_gray_screen&xtcr=2
ATI has acknowledged problems with drivers for 5xxx series (crashes, grey screens, lines). They released a hotfix for the 58xx series, but as of right now, these problems are not fixed for 57xx.
Personally, I wonder if ATI is having some quality control problems with the 5000 hardware that they don't want to admit. They may be hoping they can stabilize the bad cards by tweaking voltages or timings in the drivers.
Just my 2 cents. I know a lot of other people's cards have been fine, and maybe I just had bad luck. I was very happy with my 5770 until it broke. For price, performance, and features, the 5000 series currently can't be beat. That made it a hard decision to go with the GTX 260 but in the end the stability and reliability of the card was more important to me than anything else.