Where is the cabin air filter on a 2005 silver Chevrolet

The answer is --- You don't have one! That's correct. There is no cabin air filter on the 2005 Silverado from Chevrolet. It's location is "not in Your vehicle". Starting in the 2003 model year, the passenger compartment air filter is no longer offered as an available factory option, due to GM redesigning the HVAC case and removing the cavity for the filter. While You'll see a replacement filter offered in the GM parts catalog, there isn't actually any provision for installing it. Now, if You're the type of person who doesn't like being told "No" (and You've not gotten nicked for it yet), You can cut a hole that's 1/4 inch less than the cabin air filters that are listed as compatible with the 2005 'Rado, and back from the front edge a quarter inch as well, and then angle the filter, bowing it a little, to install in that. This is, naturally, not a supported configuration by GM.