The FX 8350 is a pretty power hungry CPU, and most of the lower end AM3+ boards don't have the VRMs needed to run the CPU at full speed without running into problems. Usually you'd encounter throttling though, where your CPU clock would constantly bounce between 1.4 and 4.0 GHz as the VRMs struggle to remain cool, that usually doesn't cause shutdowns.
The M5A97 R2.0 only has a 4+1 phase VRM, which isn't good for the 8 core FX CPUs, but they do at least have heatsinks on them, so they shouldn't be overheating too badly. I wouldn't recommend attempting an overclock with that motherboard. Monitor your temperatures with AMD Overdrive, if your thermal margin is hitting zero, then that's likely the cause of the problem, if you don't have a...