Finally, this long a waited game will be soon on both European and American PSN on December 17th. The demo will be a demo of the first non-prologue game.
Here is a little more about the demo from JoyStiq:
"In Europe, the demo will allow players to enter the "GT Academy Time Trial" contest, in which the top 20 players from select countries 7 will be eligible for a chance to enter the GT Academy. The GT Academy training program will prepare the ultimate GT fan to compete in the European GT4 Cup in a real race-spec Nissan 370Z. In America and Canada, the winner of the time trial will get a trip to the Indianapolis 500. Sure, these are tantalizing grand prizes -- but we're more excited to see that GT5 is becoming a real game. Now, how about a release date?"