Is the graphics card overclocked at all? If yes get back to stock.
When does it crash? Gaming or desktop?
You should download GPUz and monitor the temps and voltage. Is the fan on full or idling?
Unplug and reconnect all power connectors, its an easy thing to do. Make sure the 5870 fan isnt clogged with dust bunnies.
Did you change anything recently? Any apps, anything?
If everything is good you need to start testing the basics. Use memtest or Prime to exercise the cpu and memory - that needs to be verified before you assume its the gpu.
Assuming that passes then you need to test the video card. There are programs for that. Monitor the card with GPUz running.
Video cards crash as a result of - not enough power, too much heat or something has failed. Check for heat buildup first, then if ok replace the PSU and see where that takes you.