The C5 Corvette is a hoover. It quite literally drives down the street sucking air up and shoving it through the radiator to cool the car. This works quite effectively and manages to keep the car low profile... but it also sucks up a ton of debris from the road! Thus, if you're looking to help your car stay cool and happy, keep reading!
So we've identified the problem. let's start with the simplest way to tackle this: You can get 80% of the results with 20% of the effort simply utilizing an air compressor and a very long air blow gun. Most folks will have an air compressor for various tasks like inflating tires, and if you don't here's your perfect excuse to treat yourself to one!
With this airgun in place you can reach down and blow air through the radiator and AC condenser through the fan shroud. It should go without saying you do this with the engine off of course. You can also sneak the air gun up through the bottom a bit if you can get the car slightly in the air. It should also go without saying if the car is in the air be sure it's chocked and secured with a jack stand so it's safe to be under. Also of important note is to set your airgun pressure to something normal, as 150psi of high volume air pressure applied directly to a radiator can damage it.
This should let you get MOST of the debris out of there and restore your cooling capabilities. Still though... you can do more!
Removing the air intake and radiator top mount will allow you to gain pretty good access to the radiator. In the picture above you can see the air intake going over the highlighted green box. Follow whatever normal procedures you would to remove this part of your air intake, which should now great you clear access to remove the top mounting bracket. In the picture there are two red arrows, indicating where 2x bolts are per side. With those removed, the radiator top mount should be easily removed to allow excellent access into the area.
Now... if you're really fastidious and want a near OEM level of cleaning... you can remove the radiator ducting. You'll need to disconnect a few sensors and clips and screws from the shroud itself, along with remove any remaining parts of the cold air intake system. With all of that removed the air intake should just pull up and out of the car. This level of access combined with the air gun should allow you to make short work of any mess remaining in there!
