500 Watt PSU Concerns
I have a 500W Coolermaster PSU and has worked well for about a year now. I currently have an AMD FX-6350 and an AMD Radeon 6670 installed. No problems at all. Though, I am thinking of upgrading to a 7870 here soon. Because of the much higher power consumption of the card, I was wondering if a 500W PSU would, realistically, be enough for both AMD parts.
Replace it. You're never going to run that card with that PSU stable enough. If you want an excellent quality PSU, which doesn't cost an arm and a leg and is 550 watts, I recommend this one -
XFX Core series 550w 80+ Bronze Certified PSU - http://pcpartpicker.com/part/xfx-power-supply-p1550sxxb9
I have this personally and I could not be happier with it. It's made by Seasonic and is considered the best value 550w PSU available.
If you are talking about upgrading from the 6670 (400W required) to the 7870 (500W required) then the answer is yes. The graphics card manufactures assumes a 125 TDP chip for their system requirements.
I would not suggest the Coolermaster PSU. They make good computer parts but their PSU's are hit and miss. Since you already own it though, I will make the assumption it will work as advertised.
The CM PSU does meet the minimum requirements for the HD7870. You should be okay for now.
However, dottorrent brings up a good point in that you should consider getting a better PSU. CM is not known for producing good PSUs. The recommended XFX, or any Seasonic that meets your wattage requirements would be a far better choice in the long run.