Can this desktop play Skyrim and Battlefield 4 on max settings?

Don't listen to Ashley. I have a 7770 overclocked which is weaker than the 650 and with my 4.2 GHz i5 4670k I can run skyrim everything maxed out very easily. BF4 should work on max-near max settings. Buying a 770 is a overkill I think but i would still recommend buying a better vid card as it should be more future proof esp with the new games coming out.

No, You would need a much better graphics card for these sort of games, can i recommend a 770 or above.