@2KforeverC5 the changing of the diff fluid is one of those jobs that takes more preparation than actual work.
Jack the car up and secure it with axle stands, wood blocks whatever have you. Just make sure the car cannot move in any direction. You need it up fairly high to comfortable do the work.
There are two plugs on the C5 diff one on the bottom to drain one on the top at the back to fill. Both of these plugs have unique"crush" washers, the washers were the cause of mine leaking. The washers are available from GM and a stupid expensive, other types might work but not sure.
I used Mobil 1 gear lube with the limited slip additive already in. The gear oil is very heavy so I got a pail of very hot water and put the bottle in that. With the pump screwed in and the bottom plug re installed I started pumping the marine pump with the hose just barely inside the filling hole. What ever you do do not drop the tube inside the housing, everything is very slippery and the pump has enough pressure to blow the feed tube off the connection.
Once the housing is full replace the top plug and washer. These things have a specific torque value but I will have to look it up. Clean up the housing inspect the side seals where the axle shafts coming out to the housing (notorious for leaking).
Once the car is back on the ground you need to do figure "8" to ensure the additive has covered the clutches. GM also suggests NO full throttle runs for I think 200 kms.
Great to see Doug's long ago thread still pops up with great information.