My PSU is a Corsair TX950 by the way. I managed to run 3DMark 11 and the Crysis benchmark for around an hour each at 950MHz @ 1.200V with no problems at all. It just seems that it doesn't want to mine or run Furmark when it's overclocked because it keeps crashing after a minute or 2 at the most.
I've posted a screenshot of GPU-Z and HWMonitor after mining for about 20 minutes. The screenshot below is with the 5970 running at stock clocks and volts. Some of those temps seem a bit high.
Now after an hour of mining the VDDC temperatures are at 120°C, still at stock clocks.