Where is the thermostat for 2005 Chevy Silverado 5.3?

The thermostat for a 2005 Chevy Silverado 5.3L engine is located on the engine block, behind the passenger-side (right-side) engine cylinder head. It's not easily accessible and requires removing various components to reach it. You'll likely need to remove some hoses, possibly the water pump pulley, and potentially other parts depending on your specific tools and access. A repair manual specific to your year and model will be invaluable for this job.