Generally speaking the Hz of a monitor limits the number of FPS that can actually be displayed by a monitor. 60Hz means that the video card transfer data 60 times per second to the monitor. That basically means a max of 60FPS. A 120Hz monitor can display up to 120FPS.
The Radeon HD 5770 is too weak to play games at 2560x1440 resolution. See following link for benchmarks of the Radeon HD 5770 with maxed out graphics in games and running with a Core i7-920 @ 3.8GHz.http://www.techpowerup.com/reviews/AMD/HD_6670/5.html