So you have this issue with other games?
Could be your TV/Monitor not coping with the resolution and going black.
Had the same issue with my LG Plasma. Turns out that if I selected the first of the 1080 options it was fine, but had issues with 1080p
I now run it on a 23inch LG LED monitor, and it is the best picture I have ever used.
Instead of necessarily accepting 720p for GT5 (and everything else) - there's a couple things you can test out.
Firstly - go through Settings -> System Settings -> Restore Default Settings (this will only wipe settings, not data.)
Then, if you haven't already, go through Settings -> Display Settings -> Video Output Settings and choose Automatic.
Depending on the outcome, then go through the above, and instead of Automatic, choose Custom and HDMI and alternately DESELECT 1080p / 1080i and see if either work for you.