Well, indeed you will notice a significant increase in performance by upgrading from HD 5770 to a 7700 or gtx 650 ti boost. The question is "Do you really need it?". Your system is well enough to avoid a bottleneck and any of the above mentioned cards will give a performance boost ,but before you buy, consider consulting your resolution. Definitely a HD 5770 is not enough to meet high-ultra gaming settings and at the same time give decent fps. It all depends upon the resolution u are playing with. A hd 7700 is good enough to give decent fps.(on high-ultra gaming settings ) if resolution is 1400 x 900 or lower , a gtx 650 ti (not boost) is good enough until resolution is below 1600 x 1080 ,and if resolution is higher a gtx 650 ti or hd 7790 should be considered , an hd 7850( which costs the same as gtx 650 ti boost , gives better performance performance even at higher resolutions.
Now its upto u to decide which one u choose. Your rig's configuration is nice and will utilize the gfx fully. But be careful, if u r running games at high resolutions, go for 2 gb model even if it costs more.This will ensure u do not run out of memory while gaming. Also consider installing some system fans if you go for an Hd 7850 or Gtx 650 ti boost. By doing this ,you will be able to overclock these and get enjoyable gaming performance.
I am reusing my old coolermaster 690 case and I have 2 120mm side fans, 1 140mm front fan, 1 120mm rear, and I am adding a second 120mm to the top. Also, I will be using the noctua nh-d14 for the cpu. I think I am going to hold on to my current card until I can afford 2 GTX 650 ti's and possibly a new psu. Thanks Everyone for helping.:)