You just need to replace your video card. Id get a 560 ti ($230) or a 670 ($430). 670 is 2x faster than the 560. A 560 will probably be future proof for another year or so running things at 1920x1080. It can run battlefield 3 at max almost comfortably at 1920. SWTOR is a joke to a 560. A 670 is meant to run most games on the 5000 resolution. You'd probably want to look into getting a better cpu and youd have to replace the motherboard as well because the new cpus are of a slightly different shape. probably looking at 200-300 for an i series cpu and a motherboard for it. You dont really need anything better than a quadcore or i3 (i series is probably like $40 difference for like 30% improvement over quadcore series) or so if you wanted to save money. Video games are mostly graphics card dependent. Cpus are mostly for running more programs at once or encoding videos to upload to youtube. They have a small effect compared to graphics cards when actually running games.
High End GPUS such as 560 and the 670
Heres also a general guide to computer parts