There are a few minor quirks with the c5 some of which have been addressed here,as well as a good deal of info on the c5 technical section on this forum.
As mentioned, it is a good idea to have the whole vehicle checked out by a qualified tech, and change all the fluids with fresh stuff,is a good idea as well.
Another good thing to do,is to run the computer diagnostic codes on the dic which is simple to do.
1) Turn on the ignition but don't start the engine.
2) Press the "reset" button to turn off any warning messages
3) Press and hold "options" , press "fuel" four times within a 10-second period.
When first engaged the on-board diagnostics go into an "automatic" mode.
The computer will show two kinds of codes, "current" and "history," designated "C" or "H".
A current code indicates a malfunction is present in the system whose module is displaying data.
A history code indicates a past problem.
When the screen displays "manual diagnostics," select the desired module by pressing the "options" button
to go forward or the "trip" button to go back.
Press "gauges" to go forward or
"fuel" to go back for each code under a module.
Good luck with the "new" z and post some pics when you can. (gotta love that red)