I think it will vary from franchise to franchise how long a particular game has its multiplayer servers up. Some series such as Battlefield and Half-Life still have their servers up for the first entry in their respective franchises despite being more than a decade old, on the flip side some EA games only get a two-year lifespan at maximum with regards to their online services.
With regards to GT5, there are a handful of things that aren't in GT6 that might be little incentives to play IMO, such as the Top Gear Test Track or a handful of cars that oddly didn't make it to GT6 (Jensen Interceptor anyone?). The thing I am wondering is if PD is going to release one final patch to allow the handful of items that only appeared with online connectivity, for starters one thing is the standard cars that don't cycle through the UCD and only appeared via PD through the OCD (the newer 2010 Jaguar sedan or the standard Enzo for anyone interested), but most importantly I am hoping such a patch would unlock all the museum cards as the nature of acquiring them requires online connectivity.