I don't know if you can compare aircraft tyres with car tyres, but considering regular car steel belt radial tyres should be changed every 5~6 years (irrespective of tread wear, I might think twice about fitting something this old.
AFAIK, that recommendation for car tires is due to potential progressive UV damage (sidewall checking) to the tire due to prolonged exposure to the sun. If the car is kept in a garage, and the tires otherwise well cared for (e.g., the car is used occasionally), they will last a LONG time.
The tube is not exposed to the sun, so unless it is otherwise damaged, it may well be in good, serviceable condition. OTOH, the tube, tire, and airplane mfgrs' recommendations should be followed where applicable.