I had two Sport Trac's and never had any tranny issues, however I am also aware of the number of people here who have had problems and some searches on the Internet will yield a lot of information that points to a lot of problems with the transmissions. These problems go all the way back to the 4 speed automatic version that preceeded the 5 speed overtdive and even the newer 6 speed overdrive. They even put sensors in the 5 speed to detect the slipping problems and blink the O/D light, but most have found that it's too late, the tranny is toast by then.
The problem originates in the valvebody (hydraulic brain) of the transmission with 2 problems, sticking solenoid valves, and blown gaskets, which cause delays in shifting that lead to slipping and excessive damage to clutches and bands. If you can detect the slipping early enough you can replace the valvebody with a newer/upgraded unit and perhaps replace the weakened solenoid valve pack for about $400-$500. If the slipping goes for too long you will need to have the tranny rebuild.
I used to know a web site of a performance tranny shop in California that would give you a Sport Trac 5 speed automatic (5R55E) rebuilt for racing and an end to the slipping problems for just $2400. There was a core charge and you had to ship your old tranny back, but I don't know what that cost?
...Rich