I am planning on building a gaming pc with the amd a8-5600k or the a10-5800k. But i want to know whether these processors are good enough so they can still play games in 2013/2014
As long as the xbox 360 is getting games, they will be good enough.
I'm sure AMD didn't design these APU's to automatically die once your computer calendar strikes 2013
Jokes aside....lol you're asking if these will play new titles coming out in the new year?...only time will tell, I'm sure they will, if you only play on one screen and set the quality to low or something, etc.
The A10 will definitly work for the foreseeable future of 2013, but you may have to lower your settings a bit. If you can stand to wait, the AMD A10-6800K Richland Series comes out in June, and the preliminary numbers are looking really good. From what I have researched (what little info is available) it's going to be a pretty good one-up on the 5800K, but I would take all the numbers at face value until more information is released.