My C5 recently was exhibiting hydraulic clutch problems.  It was not releasing all the way causing hard shifting and grinding gears!  I checked the fluid in the master cylinder and it was at the right level but it was dirty!  It was dark gray and pieces of something were floating in it.  After posting a question to the CorvetteForum, several other C5 owners were exhibiting the same problems.  Is the seal on the cap deteriorating?  Is heat causing this?  Who knows?  This problem seems to happen in C5's that are 4 years old or older and the symptoms start to appear when cold weather comes around.

Well, after changing the fluid in the reservoir several times using a turkey baster, I got the clutch to operate sporadically good, but it was still having problems.  After consulting the Service Manual, I decided to bleed the clutch, which resulted in a 100% improvement. 

UPDATE July 2002: My car had this problem return after several bleeds. The actual cause of the problem was a faulty slave cylinder. It had a slow leak. After a few weeks, the clutch was slipping due to fluid on the disc. Click here for a picture of the disc and here for a picture of the flywheel. I had Corvette Specialties of Eldersburg, MD perform the work due to the effort required to remove the drive line. I had the Z06 clutch kit installed for a grand total of $1300. :-(

First, clean all the dirt and debris, if any, from the clutch master cylinder cap to ensure that no foreign substances will enter the hydraulic system.
 

Remove the clutch master cylinder reservoir cap with diaphragm.  Fill the reservoir with clutch hydraulic fluid (DOT 3 brake fluid or GM P/N 12345347).
 

Raise and support the C5 using my instructions. 
 

Remove the intermediate exhaust pipe.  To do this, you must first disconnect the O2 sensor cables.  GM recommends that you disconnect the batter before performing any electrical connections/disconnections.  I left the battery hooked up and I was fine.  The connectors are located above the exhaust pipes just to the rear of where they connect to the exhaust manifolds.  Remove the blue retaining pin.
 

And, disconnect the wiring harness.
 

     Then, remove the retaining clips.
 

Now, remove the 3 nuts which hold the exhaust pipe flange to the exhaust manifold.  There are 3 nuts per exhaust pipe that need to be removed with a 15mm socket.  They are torqued to 20 Nm or 15 lb ft.  I suggest leaving one nut on each pipe, loosely, so that you can disconnect the rest of the exhaust system first.  Once all the other bolts have been removed, and the rear of the exhaust lays on the floor, you can easily undo the 2 loose nuts and lower the rest of the exhaust.
 

Then remove the exhaust bolts at the other end of the exhaust pipes.  There are 2 bolts per exhaust pipe that need to be removed with a 15mm socket.  They are torqued to 50 Nm or 37 lb ft.  My exhaust gaskets were in great shape so I'll reuse them during reassembly.
 

Then, locate the forward exhaust hanger, just behind the clutch bellhousing.  There are 2 15mm bolts that need to be removed.  They are torqued to 50 Nm or 37 lb ft.
 

Next, remove the 2 rear exhaust hanger bolts.  These require a 13mm socket.  They are also torqued to 50 Nm or 37 lb ft.
 

Undo the 2 loose nuts from the front of the exhaust assembly and lay the exhaust on the floor.
 

Slide the exhaust assembly out from under the C5 and put it out of the way.
 

Next, locate the 36 bolts that hold the Driveline Tunnel Closeout Panel in place.  This is just above the exhaust assembly you just removed.  These bolts require a 5/16" socket.  They are torqued to 10 Nm or 89 lb in.
 

    Remove all but the rearmost and forward most bolts.  Then, remove the rear, and support with a leg or a 2x4 while removing the front.  This panel is not heavy but it is awkward.

Place the panel aside.
 

This exposes the torque tube.  Here's a picture from the front, facing the rear.
 

Face the front of the vehicle and reach your hand up around the torque tube until you feel the bleeder bolt.

    Here are some close up shots of where you need to locate the bleeder.  The red arrow points to the location where the bleeder is, above the torque tube.  The blue arrow shows the clutch line.  The slave cylinder is located inside the torque tube / bellhousing.

I removed the lower bellhousing / inspection plate to show you what you how the system works.  You DO NOT need to remove this plate as part of the bleeding process.  The red arrow points to the bleeder.  The blue arrow points to the hydraulic line.  Here's what the slave cylinder looks like outside of the tube.  When you bleed the clutch, it's inevitable that you're going to get clutch fluid inside the bellhousing, but it will not come in contact with the clutch.  It will run out of a little drain hole in the bottom of the inspection plate.

Put a 7/16" wrench on the bleeder bolt and have an assistant depress and hold the clutch pedal.  Loosen the bleeder about 1/8 to 1/4 turn and retighten.  Do not remove the bolt.  Fluid will shoot inside the torque tube tunnel and run down your arm, as well as inside the bellhousing.  Have your assistant release the clutch pedal only after you have tightened the bolt.  I found that after I bled the system, my assistant had to pull the clutch pedal off the floor.  But, it operated fine after that.  GM recommends doing this 7 to 10 times until you have bled any air or bad fluid from the system.

  Every 3 to 4 bleeds, add more fluid to the reservoir in order to prevent removing so much fluid that you draw air into the system.
 
 

When you have completed the bleeding procedure, wipe any and all excess fluid from underneath the C5.  This stuff is flammable and you don't want to catch your C5 on fire.  Then, reverse these instructions to reinstall the Driveline Tunnel Closeout Panel and the Exhaust Assembly.  Fill the master cylinder reservoir to the maximum fill line.  Then lower your C5, clean up and test the results.
 
 

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