The C5 can easily run the Z06 tire sizes, and they can even fit on the stock rims, but I would recommend that you get the Knock Off rims that are like the Z06, or the ones that look stock, but they are chromed and are 1" wider front and back. You can get these for about $1000.00 and they do fit the vehicle much better and look much nicer than the polished rims! They really helped me loose some of the spin on luanching the car, and MAN what a difference in handling, plus if you get the non runflat tires, your car will ride a little softer, and be much quiter than the stocker, you will absolutely love them as much as I did.
Oh, yeah, the diameter of the tires is a little bit different, but you do not need to recalibrate your speedometer, the change in accuracy is very small.
One last thing, the knock offs are as strong as the stockers, and the offset is set a little bit better. I had my car up to 180mph on a long open freeway, and the rims held up fine, just in case you were worried about the rim strength.