Well a 650 Ti averages 29fps on Battlefield 4 at 1080p Ultra with a Core i5, so I'd imagine with an A8-5600k (which is more or less a Phenom II X4)
you'd see 30-40+fps on medium.
I'd seriously recommend getting at least an AMD FX-6300 as you are not using the integrated graphics of the A8 and that is the main reason to buy that chip. The FX is only $20 more than the A8 on Newegg so I'd definitely recommend the FX