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When you lower the car you should get an alignment. However lowering the rear 1"+ will lead to two potential problems, the first is bottoming out the shocks--hitting the bump stops. The other is when you start going very fast. The C5 needs at least 1/4" wedge front to back (being higher) or it becomes more like a wing and at triple digit speeds the font end starts to lift. Most usually lower the car to get the frame closer to the top of the wheels. However when you go more than 3/4" lower you might have to address other problems. If you HPDE or AutoX the Corvette the body roll at speed comes into play and can cause some handling problems that will need to be addressed.
Remember to turn each side an even number of turns. Do not attempt to level the car out by measuring the fender height, and adjust a particular corner independent of the other. If there is a variance currently, then the variance needs to remain after lowering.
Seven to eight revolutions will give you roughly an inch of lowering. It will not lower immediately, and needs to be driven roughly 50 to 100 miles to level out. It's advisable you get an alignment done, however if your tires are nearing the end of their life you may wait to lower your car, lower it prior to getting new tires, and then having the alignment done then.
thanks, I think Ill leave it alone, did that to my mustang, liked the way it sat...not important enough to screw something up....plus, I just built a new garage driveway, and not sure, but I just barely make it without scraping, got lucky...
One other item to check is weight balance shift. If you were to lower only the rear, the weight balance (distribution) could shift. You would want to lower the car in such a way as to keep the distributed weight of the car equal on all four tires.