The PS4 equivalent gpu is an HD7850 which goes for like 150 dollars maybe less. Absolute cheapest scenario is like this:
Case + PSU = 100 bucks
HDD + Optical Media = 100 bucks
That leaves 150 bucks for the platform CPU/RAM/MOBO. Even the cheapest Athlon based platform costs more than that. Even then, you'd still have to spend some extra cash on some case fans, maybe a cpu cooler, because the stock one sucks balls.
So probably not for 500$. But for 700-800$, you can make a PC that destroys all consoles.