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I have a manual 2002 C5 with 65k miles which I recently bought, unfortunately without any service history. All I know is in the last few years it was not driven much and little to no service was done. I took it to a corvette shop and they suggested: 1 Oil Change, 2 Coolant Flush, 3 brake flush and 4 clutch flush.
I am in a weekly car care course with access to a lift and an experienced genernalist mechanic.
As there are others in the class I likely can not get all 4 items above done before the class ends.
What order would you suggest I do them in considering, cost savings, access to a lift, access to a mechanic, other.
Note my skills and experience are both low as of now.
They are all four excellent starts. Unless clutch has been fitted with a remote bleeder, flushing the clutch hydraulics is significantly more difficult than the others. Oil change is easy, but radiator drain plugs have been known to stick, sometimes to the point of breaking.
As to order, they are all about the same importance. Motor oil doesn’t really go bad very quickly, but I have had both brakes and clutches have issues with bad brake fluid, which really does pull water out of the air. If I were doing mine for the first time again, I suppose I would do brakes, clutch, oil, coolant.
Given your limited access to a lift and a mechanic I would do the clutch flush first. It's very challenging to get to the bleed screw on the slave cylinder. I think the mid pipe might have to come off.
Oil can be changed at any oil change place but you cannot do it without access to either a lift or a pit. Even if you run it up on ramps in the front the drain is at the front of the pan so you'll probably only get 2/3rds of the oil out if you did it that way. And that's assuming you're skinny and can actually get under the car. I have Race Ramps with 12" lift and it's still not practical to do any serious work under the car.
I would also change the transmission and differential fluids, and any other fluids.