2007 Mustang GT automatic transmission has no 4th, 5th or reverse gear

Rebuild or replace transmission.

This is a 5R55S automatic transmission, which was used for a number of years by Ford. There have been valve body issues and servo issues with this transmission -- some of which are repairable in chassis, and some not. Testing is really best to star with -- electronic transmission testing by a technician with good diagnostic equipment and experience. Indeed, it may require a tear down and rebuild, but maybe it could need something less comprehensive. It'd be worth looking into.