How much does it cost to repair a bent car frame?
First thing you need to do do is step back and take a deep breath. Your Explorer has what is called a uni body over frame construction and at a 5mph collision it “could” have moved some of the sheet metal out of alignment. The frame is probably not bent and if it is, then it is not a big deal to fix it. When choosing a body shop for the repairs, ask if they have a computerized measuring system, that will ensure that any damage will be picked up by the computer and the repairs can be made correctly. Before you make your next move, I would contact your insurance company for an estimate, they may tell you to get three estimates on your own and while you are there ask about the measuring system. If it just some aligning of the sheet metal and some minor paint work, probably in the $1000 range and if some parts need to be changed then of course a little more.
