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The mirror in my C5 is connected to a ball joint which is connected to the base of the mirror via another ball joint. The base of the mirror is connected to the windshield via a set screw to the mounting point which is glued to the windshield. You need to look at the base where it connects to the windshield for a set screw to undo. I don't recall if it is a torx or a hex but there is a set screw right on the base at the windshield and it is visible. I know that this was the case in '97-'00, I'm not sure when they may have changed the mount for them.
Paul
***edit*** I forgot to mention that my C5 is a '97.
Here is a picture of the assembly in my car. Click to enlarge.
I have a 2004 coupe i didn't have any set screw there was a clip that you need to get from the bottow where it attaches to the windshild. you can either pry off of the windshield and risk breaking it -OR- do what my uncle did...he took a needle nose plyers but the 90 degree angled one and wrapped one tip of the plyer(the one that rests on the mirror) with duct tap so it wouldn't scratch...while compressing the clip push the mirrow down ward...you should be able to see the slip through the front windsheild with a flash light when it looks like it it compressed enough slide upward and it should slide right off
p.s. make sure the plug for the map lights is unplugged
click the pic to enlarge
the end of the needle nose plyers WITHOUT the tape goes on number 1 (you can actually see the clip in the pic that needs to get compressed)
the end WITH the tape goes on number 2 (thats only so you don'e mess up your mirror)
i told you it wasn't easy...i took the same chance you did...before i did i went to a glass place and they couldn't even do it ! don't worry insurance should cover it
man, i would not think it would be that difficult to take off...it is cracked but it is not htat noticable since it where the glass is tinted. I will try to take it off again tonight...