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The C5 wheels will have a different offset and will sit further inside the wheelwell than the stock wheels. They will bolt on as they have the same bolt pattern and the early lug nuts will work (all have a 60 degree taper).
You should check for any possible rubbing interference in the front (especially at the frame rails and the bottom corners of the wheelwell. Also check out back for any interference with the rear suspension components.
If you look at the chart in the link, there will be almost a 3/4" difference in offset with the front C5 wheel and an inch for the C5 rear wheel.
Spacers and adapters are different pieces. A simple spacer is a ring that slides over the studs and the wheel goes on next. This effectively reduces the length of the wheel stud that goes thru the wheel and may not even allow you to get the lug nuts threaded on sufficiently to tighten them properly. Spacers also extend the wheel "load" further out on the studs and that could cause studs to fracture. Not a good thing to have happen
Adapters bolt to the hubs and have their own studs that are use to attach the wheel. These are much safer and stronger when using wheels of different offset. Expect to pay a bunch more for adapters but it is money well spent.
Go with a set of adapters. Given the difference in offset, spacers will not be safe and may not even work.
I've been running 1 1/4" adaptors on all 4 corners for the past few years. The Y2k rims I have on my 87 vert sit flush with the body and I've had no problems.