yeah... you're a bit top heavy... you can go with a much slower cpu and still not cpu bottleneck that 7770.
if your budget is $380 for cpu/gpu, (220 = i5, 160 = 7770)
i would go with a FX6300 (120) and a 7870xt (240) -> that combo will nuke the i5 combo in games. Granted the math isn't that simple... with the fx you'll need a cpu cooler and have to overclock it. if that isn't something you want to do, then i suggest you figure out some way to get a better gpu into your system.