I just bought a 1990 rx7 FC S5 that came with 15x7 inch rims with 35mm positive offset. The tires on it are undersized and I was wondering what the largest size tires I could put on it would be.

 

205 is probably the biggest you want to put on a 7" wheel

 

Actually a 215/60 (25.2") as well as a 225/60 (25.6")can be installed on a 6.5"x15" wheel, but the
diameter increases so one would want to see how they would look on the car, 205/60-15 (24.7").
Best best is go to a different wheel size and have more selections.