I don't think you'd be able to turn down the settings FAR enough for smooth game play at 5760x1080. Maybe if the 3 monitors were 1024x768...
Generally Eyefinity requires a high end card... or two.
With a R9 280x you will be able to, anything less is going to be tough. You will find the res too low or the fps will be unplayable. R9 280x should be able to run 3 monitors on med setting easy with decent fps.