at those resolutions i would certainly recommend the 5770. its a fair bit more powerful than the 5750, and at those higher resolutions can easily make the difference between playable and unplayable.
Totally agreed. a 5750 might be a good choice at around 1280 x 1024 resolutions but as you start cranking up the resolution the 5750 just won't cut it. With LCD panels you also want to use the panels native resolution to avoid the stretching of the image which can lower the picture quality noticeably. Even though you might get "better graphics settings" with lower resolution selected it still might not look as good as with higher resolution and a little bit lower graphics settings. So with a 1920 x 1080 panel you should aim to get a card that can actually play the games well at that resolution.