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I need to do the same fix. I can't tell you off the top of my head what the fix is, but if you do a search for "rocking seat fix" You should be able to find what you are looking for.
:EDIT: Whoa, I just reread your post. It moves 5 inches? That doesn't seem like the typical rocking seat problem.
Your seats are moving 5" !?! You need to do more than the "normal" rocking seats fix, something else is wrong like your tracks are broken. This sounds really dangerous, at least to me, I recommend you take out your seats and really look them over good.
Are you talking about the base of the seat moving or the back of the seat moving? If it is the back of the seat, that is normal and all C5's do it. If it is the base you need to replace the seat tracks or perform one of the DIY's that you can find on the forum to refurb the track.
I AGREE!!! Holy cow, man. If your base is moving 5", that's definitely a safety issue. The typical "rocking seat" fix is only caused by a worn plastic piece that allows the base to move usually a small fraction of an inch (just enough to be noticable on acceleration/deceleration). If you mean the seat BACK moves 5", there's nothing to worry about, it's normal. But if your base is moving that much, you REALLY need to take the seats out (go to Vette Essentials website and follow the instructions for removing the seats - under installation instructions for new seat covers) and inspect the entire track mechanism for something seriously broken. You should do it today - don't wait until you have an accident and knock out your front teeth on the streering wheel!!!