[XenonSurf]

If you are plugged to monitor with HDMI cable, then change to DVI-D or DSUB cable. Try this first.

As a stock game of SH5 you have the version 1.2.0 or you have patched it to that version; and you are running in admin mode, right? If it doesn't start here then don't even try to mod the game, you must first resolve.

Your GPU card is ok to run, what is your processor and RAM (but should be ok too with this card).

The game going to main menu without crashing (without ending sh5.exe in the task manager process) is most likely due to bad scaling settings, you should resolve quickly by going in the your ATI settings, set everything to default, and then try similar settings told above.
SH5 fully supports widescreen resolutions and advanced grafic settings, and Win7 is the adequate OS for it, I can hardly imagine any other reason, except here below.

Do you have other programs running when you start SH5, check this in the task manager by sorting the entries by RAM and Processor load; you may have to end non-OS processes.
What about your anti-virus: has it a gaming mode? Make sure you turn this on. Is it scanning in real-time? If yes turn this off. Best is to switch off completly antivirus and go offline before starting SH5.