Need 4 speed Shift or Shift 2 should suit your needs. I'd say Race driver G.R.I.D. but the online servers were shut down in 2011. Sad that the game came out in 2008 and they allready shut the servers down, and it was a great game too with real good graphics and it was very easy on hardware requirements. Well I guess GRID 2 is on the way...
I never played GT5 or Forza 4 but I would say Shift 2 would be closest to look and feel from what I have seen. GRID is kind of fun but ridiculously unrealistic A.I. I have always enjoyed the DIRT series up to DIRT3 except for the hockey Gymkhana crap but the rally racing is superb and the AI fully customizable.
I'm looking for a good driving game pretty much like GT5 or Forza 4 but for the PC.
Grand Prix Legends - Older game, but fantastic handling of older open wheelers. It is not the easiest game to play(NOT arcade style, but very realistic), tweaking option and the graphics are really good for the time period.
Its older, but GTR2 is has a great reputation (and its less than $4 on Steam currently). DiRT series is also great on the realism front. If you don't mind switching to an open wheel racing game, the F1 (F1 2010, 2011, 2012) games are really quite good as well.