I have been running tests with another video card (4350) to replicate a BSOD where my 5870 was getting a GSOD. It appears as though the the BSOD Error number is BC: 101. When this error occurs, your system is freezing at about 40% of the memory dump during the BSOD. This explains why your computer does not automatically restart whenever you receive a GSOD. Essentially, this error has to do with CPU voltage. Regardless of whether or not your overclock is stable, add voltage to your CPU (VCore). There is obviously some sort of connection (other than the obvious NB/SB link) between your CPU's voltage and the 5xxx card. It might not be a driver issue after all. Please test this out on your card. Add voltage to your CPU until the GSOD goes away and report back. Obviously, don't put your CPU's voltage at an unsafe level. I will remove this excerpt if it does not work for the majority of people. Try it first, it has worked on all of the tests I've thrown at it.

I think the OCN thread has explained enough the GSOD issue so if still persist then that sounds like a card problem. Send it for RMA. 
i5 3450 has a locked multiplier with turbo up to 3.9 only hence at such a low clock it should run fine at stock vcore.
OC in BIOS settings. You're asking the wrong person about safe voltage - check out first post for basic notes.

I think the OCN thread has explained enough the GSOD issue so if still persist then that sounds like a card problem. Send it for RMA. 
i5 3450 has a locked multiplier with turbo up to 3.9 only hence at such a low clock it should run fine at stock vcore.
OC in BIOS settings. You're asking the wrong person about safe voltage - check out first post for basic notes.