I have successfully installed the Catalyst drivers and hooked up my 1080p TV to the Radeon HD 5750's HDMI port and now it is working. There only seems to be one issue - most images appear OK, at least to my eyes, but text is grainy and difficult to read (not sure how well it can be seen in the picture):

It works fine with a smaller screen, and hopefully you can see it with the new pictures which are only slightly better, but images are rendered a little funny too. Changing antialiasing does nothing and changing the refresh rate only makes a slight change if any. The small monitor I have works fine. Smaller resolutions such as 1024x768 look OK but are the wrong aspect ratio.

I have tried renaming the input mode on the TV to "PC", and that helped... a little bit. Also, I tried a different PC with the same result. Messing around extensively with the ATI Catalyst Control Center also did not help. I am wondering if there is anything else I can try to increase the quality so it is more usable.