That CPU is not supported, AT ALL, on that motherboard. It's not even on the CPU support list. Usually, even boards that are too weak to really support the 8 core FX processors tended to still list them. That one does not. That tells you all you need to know. That board only supports processors up to 95w, while the FX-8350 is a 125w processor. Power phase and delivery on that board are terrible. There are no heatsinks on the VRMs. Plus, ALL of the M5A78L-M motherboards including the LX3 and other various sub models are of terrible quality, even for that chipset.
You need a better motherboard or you need a 4 or 6 core FX processor to use that board. One of these would be suitable and generally still available either new or used.
(Be sure to check when looking for a motherboard that any of the models shown below are either 990fx, 990 or 970 chipsets. A Z170 Extreme6 for example, is not going to work with your FX processor, so you want to look for the 990/990fx Extreme6, just as an example.)
GA-990FXA-UD7
Extreme6
Extreme9
Fatal1ty 990FX Professional
Crosshair V Formula-Z
Sabertooth 990FX R2.0
GA-99FXA-UD5
MSI GD80V2
M5A99FX PRO R2.0
GA-99FXA-UD3
MSI GD65V2
990FX Killer
Extreme4
M5A99X EVO (R2.0 as well)
GA-990XA-UD3
990XA-GD55
GA-970A-UD3P
M5A97 or EVO or PRO (R.2 as well)
GA-970A-UD3
970 GAMING
970A SLI Krait (USB 3.1 supported)