No, don't even consider it, 500Watts would be really pushing it for a A+ top-of-the line power supply, which your system doesn't have. Do not try to connect up the R9 nitro until you have a power supply that can handle it.
What kind of power supply would you recommend?
EVGA Supernova 650 watt NEX650G Other EVGA power supplies, XFX or seasonic, or corsair, but not CX series. 650 watts is a good idea.
I did some research and ended up ordering a Corsair RM750i yesterday. I kinda knew that it would be about time to replace the PSU as well but was on the fence about it, thanks to both of you for pushing me in the right direction.