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I'd ask for service records, especially looking for the every 5 yr engine coolant change.
The "big" cost items can be harmonic balancer and tires, which you can inspect both.
Another big cost item is the fuel pump failure, but this can not be predicted other than to "sniff" around for a fuel odor.
There were just a few recalls including the fuse box and steering lock.
You may wish to ask about those.
Lastly, 05 had a few one-year-only traits.
Including a computer module that I understand now needs to be sourced used, as production/ inventory has ceased.
I have 05, with 83,000 miles, I would look for any wobble in tensioner and make sure shifter if auto moves smoothly back and fourth, those cables are known to break, check for binding is good indication. Look at tires when replaced or manufactured.
Also check when any service was done, or car fax report.
If you have Vin number take it any Chevrolet dealership and ask for history if possible.
So what should I been aware of when I check it out - 54,000 miles, one owner.
I've had my '05 6-sp since new....just turning 60K miles & has been totally reliable. Some of the early C6's had harmonic balancer problems (wobble) requiring replacement (not mine). You don't say if 6-sp or auto, but again, some of the auto's had shifter problems. Only recall I know of is low beam headlight failure due to a broken wire in the fuse box. There was a recall notice several years ago & 'no cost' repair at a dealer....check with the owner. As in every case for a used car, check CarFax & with the VIN, you can get a work history from a dealer.
I have a 2005 for a year now. I love it, I had a 1986 C4 for 11 years before this one and I thought I lived that one.
People say the diff is weak, the LS2 is not as good as the LS3, it’s a one year ecm , etc.
Again, I enjoy it every time I drive it or just look at in the driveway. I’m not tracking it or putting sticky tires on the rear.
If the price is right and it has the options you’re looking for as well as the color, buy it and enjoy it.
Matt
one year of ownership and 36k, the convertible top has been my only issue gettin stuck on the waterfall , also shifter starting to get stuck ,happen twice