It's an optional install - you may still play Gran Turismo 5 with a 256MB basic installation if you don't have much space. Whole hog, you're going to need upwards of 10GB - and 50 minutes - free.
Amar212, a GT5 power user well known on about three forums, got his hands on the game (PAL version) and says its installation screen offers the warning that "install of game data can take up to 50 minutes". He says it took 40 minutes for him and 6.4GB at first, but since learned that Grand Turismo 5 will continue to unpack itself during playtime with the game. So keep that 10 gigs free if you're butting up against your drive's capacity.
It's an optional installation, but if you don't use it, you may expect longer loading screens. So you can do your waiting up front, or on the instalment plan. Which, like the real world, you'll end up spending more, in this case time.
Many other details about the game at the link.