No, a Hard Drive at most will affect load times, Or if you get a lot of hard stutter like 80fps suddenly dropping to 0fps stutter, thent hat could be an Hard Drive issue.
But FPS wise, the Hard Driver will in no way change your FPS, you could get the markets fastest SSD and your FPS will be the same.
I'd look else where, your r9 270x is a bit faster then a HD7870, so you should be getting good FPS in that game as the recommended GPU in a HD5770.
What kind of FPS are you getting?[/quotem
Min : 38 .. Average : 45 .. Max : 60