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Rim size isn't too important but overall diameter is.
For instance, you could run a 16" rim with a 2" sidewall tire or a 18" rim with a 1" sidewall tire. That's just an example.
I believe I have seen 15" rims on a drag C5 before. The rears had some serious sidewalls.
Quite a few on the forum run 20" rims in the back with 19" rims up front.
The smallest rear wheel usable on a C5 is 15" and even that requires the installation of aftermarket rear spindles PLUS you have to do some grinding on certain rear suspension parts to make that work. The rear brake calipers are smaller than the front wheel brake calipers so you can get by with 15" back there. On the front is a different story. The brake calipers being bigger will limit you to a 16" wheel and even those will require some massaging. CCW made a C5 drag pack with 16" wheels that were probably the best fit. Otherwise, without going to some aftermarket brake calipers, the 17" are basically the smallest you can use. A lot depends on the wheel itself and how it was manufactured. Of course, the reason for smaller wheels (especially on the rear) is to have more sidewall which gives more grip when racing. Larger wheels give less sidewall. Sometimes large wheels use tires that have almost no sidewall at all. Those are referred to as "rubber band" tires. Many prefer the larger wheel sizes but I'm old school and prefer tires with big sidewalls. Hope that helps.