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@sazam ,
As far as I know, the 2005 GT had 275/40/ R19's all around, I think that the 20's came in 06.
As far as people doing the staggered setup, be it with the rear being wider than the front, or even say 19's in the front and 20's in the rear, one must always stay within the allowed percentage of difference between the tire sizes themselves, because of the all wheel drive, as your GT has 50/50 split front and rear.
I believe that the percentage is 3%.
So all four tires should have the same diameter/circumference to a certain degree/%.