How long have you had the M5A97? Is it the original or the more popular EVO? I had an Asus P67 LE that would not quit throwing BSODs (it was so long ago, I can't remember what the error was ), and after exhaustively testing every part including CPU and RAM I ended up just tossing it. It seems it was just at the end of its life. Coincidentally, both boards from Asus - P67 and 970 - are verging on 8 years old at this point.
Are you using a stock cooler? How is the airflow in the case?
The M5A97's 4+2 can handle the 8350 just fine at stock speeds like OP has kept his at. OP says there are heatsinks so it's not the LE. That RAM does make me raise an eyebrow, though, 1600 CAS11 is old and slow and the high latencies and lack of manufacturer in CPU-Z suggest that it's an OEM part.
The XFX TS/Core Edition is a great little power supply, based on Seasonic S12II. It's just fine on quality, for the group-regulated unit it is. I wouldn't count it out as being defective, though.