Cumputer crushing after about 5 minutes while playing games

Based on your components, I would suspect the power supply first, and the motherboard second. Thermaltake makes excellent cases but not excellent power supplies. 800 watts is more than enough for that system, but not if it is poor quality 800w. I would get it checked out, or if you have another power supply to swap in, that would be the easiest way.

The second thing with the motherboard is that MSI is not the greatest quality either. It could be some capacitor or voltage regulator is failing.

A third suspect would be the video card. Gigabyte makes excellent motherboards, but their video cards are just so so.

Thanks, I'm starting to suspect it could be the motherboard because it crushes even with a single gtx295 which doesn't require that much power

It could still be the PSU. Even though it says 800 watts, it may not be supplying that, maybe never did. As they age, things go down hill. Of course a component in the PSU may have failed or is failing as well.

The other issue with low quality power supplies is that they can often supply "dirty" power. This also gets worse with age.

Once again, I would get the PSU tested if you have something like a Best Buy Geek Squad nearby or some other computer shop.

Think of the power supply as the mother of a computer. In Texas, we have an old saying. If mama ain't happy, ain't nobody happy.

Hm, I'd think the 295 requires significantly more power than a 560 Ti.

Thanks for the feedback, will get the psu tested