My pc shuts off while playing games

Hello, i very recently built a gaming pc ( about 3 weeks ago) my first time doing anything like this so please realize I may not understand alot of technical terms, anyway im 2 weeks in and im having a great time playing games when suddenely it just turns off, no warning, no blue screen, nothing just shuts off and boots itself up again so i tried playing another game it did the same thing. The problem persisted for a day and then in the morning the problem was gone so I didn't give it another thought. Fast forward one week and its happening again. I boot my system and when im watching vids or surfing the web nothing happens but when i start playing games and 4 or 5 minutes in it shuts off. I do not think this is a heat issue as I monitor my temps with programs like speccy and coretemps and only goes to 40-55 C when playing graphic intensive games. Here are my specs. My power supply is very new and is 500watts, so i dont feel that is the problem either.

Operating System
Microsoft Windows 7 Professional 64-bit

CPU
Intel Pentium G850 @ 2.90GHz
Sandy Bridge 32nm Technology

RAM
4.00 GB Single-Channel DDR3 @ 532MHz (7-7-7-20)

Motherboard
ASRock H61M-HVS (CPUSocket)

Graphics
P246HL (1920x1080@60Hz)
1024MB GeForce GTX 550 Ti (Gigabyte)

Hard Drives
466GB Seagate ST500DM002-1BD142 ATA Device (SATA)

Optical Drives
TSSTcorp CDDVDW SH-224BB ATA Device

Audio
NVIDIA High Definition Audio

Any advice and help would be much appreciated.