Is your CPU, system RAM, PSU stable ? If unsure, start making some tests.
Have you installed all necessary x86/ x64 redistributable, patches, physx, etc. ?
Try disabling ULPS.
Have you clean installed drivers as described here ?
Is windows up to date (with optional updates as well) ?
Are your HDDs in good condition ?
Does SSD have the latest firmware ?
PSU +12v rail value ?
My point is, if you are absolutely sure that no other component/ driver is outdated or has issues, then you can isolate the issue to bad amd drivers, or to a faulty gpu.
If you have the luxury to test that card on another stable computer, or to try a different card with your computer, then you will have a better idea.
If you want to spare all the fuss, then rma the card and test the new one.
gigabyte X58A-UD3R rev.2, core i7 975 3.9ghz (stock voltage), windows 8.1 64-bit, corsair 12gb DDR3 1600mhz 7-7-7-20 RAM, xfx HD 5970 + gigabyte HD 5970 (950mhz/ 1100mhz), coolermaster ultimate 900w PSU.
AMD Catalyst 15.4 beta