Computer shuts down during gaming
I recently purchased an r7 250 so I could run it in dual graphics with my a10-7850k, but whenever I play a game (alien isolation) for about 5 or 10 minutes the computer shuts off, leaving me with a black screen. I am running my gpu and cpu at stock speed and my CPU temps are well below 50 degrees while playing. I am using a cooler master hyper t4 cooler. I am also using a corsair 500w power supply (CX500M).
It sounds like either heat (which from your description, you've covered off) or PSU.
Corsair's CX line isn't very good at all.......Tier 4 (http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html)
I think, unfortunately, you'll need to replace your PSU. The GPU has increased your wattage, and the PSU can;'t provide adequate levels/consistency (despite Corsair's claims).
Here's a good replacement that's on sale.