A lot of specialty lumber yards have plywood in 5x5 and 5x10 sheets. Marine or aviation grade plywood will stand up just fine. I've had the same ratty old sheet of exterior grade plywood in my bed for 5 years and it hasn't rotted out, fallen apart, or done anything but get a bit slimy. Its protected by a glaze of motor oil, sap, scum, and huberis. It's about time to retire the truck to a life of dignity and paint it and put a real bed back in it.
