The Athlon 64x2 is the first Dual Core desktop processor. There is a about 4 separate code-named variants of this design so the older ones are not as fast or efficient. The Ahtlon II Dual Core is a bit faster yet though still not able to keep a GTX 760 or R9 270 fed with data. If you plan to upgrade your CPU/MB anyway then by all means get a new GPU. If not then i do not see a compelling reason to get any graphics card in that price range. There are benefits to having DX11 graphics card over a HD 4800 series (DX10) but those benefits would go as far as a HD 7770 or something around that Power as the Athlon just is not powerful enough.
EDIT:
Note: I used an Athlon 64x2 5400+ and an Athlon II 250. I can say that paired with an HD...