PC reboot with no error when playing games

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I know there are threads like this one but everyone seems to either find a solution that doesn't work for me or abandons the thread without finding a solution all together.

Whenever i play a somewhat demanding game afer around 5 -10 minutes my PC reboots. The screen goes black then boots back up.

I'm not sure why this happens. I can play games like minecraft for hours without problems but, for example, GTA V will force a reboot after around 10 minutes game time.

I've cleaned my case out and installed a new cooler. It was pretty hot, reaching 95+ degrees but after buying a new cooler and cleaning the case and fans my temperatures have dropped and seem steady. But the reboots keep happening.

My specs:
Aerocool Integrator 500W PSU
AMD Athlon x4 860k quad core processor ~3.7GHz
8GB RAM
GeForce GTX 960

 

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Just played a good hour of GTA V without rebooting, yet previously Kona forced a reboot about 10 minutes in.
The difference being GTA was windowed and Kona was fullscreen.

 

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Update: I've noticed the error only happens when i'm either streaming or recording using Shadowplay. Any clue why this would happen? I downloaded Xsplit to stream whilst playing games with that and I had no problems

 

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EDIT: I upgraded my PSU and now my problems have been solved