If you don't use the second monitor for gaming, but for 2d applications like surfing the next or other text applications, then your game performance will hardly be effected compared to using the 5870 on just a single monitor.
But, using two monitors together to game, literally doubles the resolution the 5870 needs to output. This may not mean that your FPS will drop in half comparatively, but there will be a significant performance drop, assuming you aren't already being limited by the CPU as it is.
If your CPU can feed a 5870 to its fullest potential, the difference in performance between 1920x1080 and 3840x1080 will be significant and obvious. If your CPU is already a limiting factor in your graphic performance, then the card will have headroom for extra load, that will decrease the negative effect that raising resolutions has on performance, relatively.
Maybe someone with multiple monitors can give their personal experience with it, but just remember that the entire build has to be taken into account when comparing these sort of performances.