Yeah it would improve your gaming experience since the A8-5600K has 4 cores while your A6 5400k only has two cores. Here's a site you can use to check the difference between both processors.
I'm still trying to figure out why you bought an APU instead of a tradition CPU if your using a discrete video card. If you would have went with an AMD 965 Black Edition for $20-$30 more your gaming experience would be so much better. But seeing how you have an FM2 socket motherboard if you can stretch your budget I would actually go with the A10-5800K or the new Richland A10-6800K.