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hey how did u conclude that ur GPU is dead !!!
anyways did u check whther all the GPU drivers are installed properly !!!
I you PSU enough to run this Card.?? i dont think so, coz it requires much power. maybe you should try out on some branded PSU like corsair or coolermaster. this maybe the main cause
If its still barely 2-5 days old, it qualifies for a DOA where the dealer/distri will swap it for you.
Did u connected the 6pin power connector on5770 each time?
I think the problem is with power supply.when you run your graphics card continuously the psu fails due to overload and may be causing problem to your graphics card.you told you have 10 system,then how many of them have failed by now?
welcome brother,good luck.