C5 Corvettes are widely referred to as "The Corvette that nobody drives." 

That statement doesn't imply that they are bad cars. It actually refers to the amount of them that have low mileage as most people, for whatever reason, keep them stored away.

The biggest issues with C5 Corvettes, and I invite @Daywalker to join in this conversation as he currently owns one, are the following:

1. If manual, the clutch job is EXPENSIVE. You basically have to disassemble the car to do it. 

2. As with any car that has them, the fold up headlight motors and gears break. GM only used plastic gears, so most owners go back with brass for longevity.

3. Electrical issues are the number one problem. From "Service Column Lock" issues to random glitches, the electricals in many of these cars love to act up. It can be very tough to run down wiring faults on these cars.

4. If it's a targa and you live in a hot climate, the fabric on the headliner likes to unglue and hang down, causing particles of foam from the insulation to blow around the car. 

5. The car uses a "u-shaped" fuel tank. In other words, for handling purposes, part of the tank is on the right side of the car and part on the left. It is connected via a fancy design and a very unique fuel pump setup. This is known to be a serious issue when the fuel level sensor goes out as the whole tank requires removal. Over $1000 job.

6. They sit LOW.

Bottom line: they are picky cars, but fun to drive when they work. I've had a few and still have a Z06. But I rarely drive it and it still acts up from time to time.

Realize that any parts come with a Corvette tax....nothing is cheap on them. 

If you can find a good one and a mechanic passes it, go for it. Just be aware that they are like Harley's: working on them is part of the ownership experience.

Yeah definitely have a mechanic check it out they can be good cars if owned by a middle-aged or out early guy with young guys generally beat him up. If it's not a one-owner car and it's had many previous owners definitely have a mechanic check the engine and transmission closely and make sure it hasn't been wrecked

I actually own a 2004 C5 coupe with the reliable LS1 engine (and with manual) and I am the second owner with currently 43,500 miles on it.  But it’s an occasional weekend vehicle and the only issues I’ve had from 13,500 miles (when I bought it) to now is failing window regular motor (both driver and passenger side) and leaking magnetic shocks.  I had all those fixed by my mechanic and they were not cheap.  If you need a new clutch you are looking at >$2,000 - I don’t need one yet but the whole torque tube and bottom end has to drop down to replace it.  I’ve been lucky not to have any of the issues Mod_Man listed but others have had it.  Owning a C5 is not cheap nor for the faint of heart:  maintenance and repairs are more costly than owning a Camaro or Mustang and you pay Corvette tax on everything if you have someone else do the work for you.  As with any performance car, you should be into it and learn as much about how the vehicle works and try to do as much as you can yourself (if mechanically inclined).  You should also be prepared to spend a few thousand dollars here and there for repairs over time - if you can’t do that, this is not the car for you.

I recommend it over a C6, C7, and C8 as it’s less complicated and more reliable (some people can get >200,000 miles out of the C5 but that’s on the LS1 engine), but I would think twice about making it your daily driver.  Let me know if you have any specific follow up questions on the C5 and I will do my best to answer.

I will leave with a final word from Master Mechanic The Car Wizard:

https://m.youtube.com/watch?v=kFfMU2NoZHA&feature=youtu.be