I don't think most of the other responders here are understanding the situation.
There is most likely nothing wrong with your car. If you are crawling along at 5 mph with the clutch all the way out, car pointed straight ahead, and then stand on it, it is not surprising that it won't burn out, particularly on a car with relatively sticky tires and a limited slip diff.
The way you do a burn out is to give the engine some revs and dump the clutch. The physics of a burnout generally requires you to build up a speed difference between the engine and the wheels. Once you have a rev difference, dropping the clutch quickly transfers the inertia to the wheels. Basically, it is not the torque of the engine alone that gets the wheels spinning, it is the torque combined with a rapid transfer of kinetic energy. Once the wheels are spinning, the engine alone can more easily keep them spinning, not just because the engine has more power once revved up, but because spinning tires have much less traction than when they are not spinning.
In short, don't expect the engine's torque alone to be enough to do that initial break of traction, particularly when the engine is bogged down at idle. (At 750 rpm, even at full throttle, these 5.0s are probably only capable of 40 horsepower).
Auto is a different situation than manual with clutch out. When you floor your auto, the torque converter allows the engine to rev up independent of the wheels...thus in and with an auto from a slow roll, the engine isn't bogged down.
Dude I spin tires at 55mph when I down shift into third and hammer on it. Go get it checked out. Maybe the owner before hand tuned it down because it was too much.
You are getting that wheel spin by establishing a difference in RPM between the engine and drive wheels and suddenly releasing the clutch. You must be hammering on the gas in the middle of the shift with the clutch in.
But he doesn't have sticky tires. He has the regular treads, non track pack non Brembo rubber with 3.31 gears.
I admit I have not driven a manual coyote, so I'm not speaking from experience here. I'm speaking by comparison, and I realize the danger in that. By comparison, my 94 Cobra would waste the tires from a slow roll with the clutch out, and it had 3.27 gears and regular ol' tires. By comparison, my manual 99 Saleen S281sc with 10-inch rims and BFG summer tires also roasted from a slow roll clutch all the way out. It doesn't make sense that the coyote with more power and somewhat comparable drivetrain and tires would not be able to roast them. That's my concern for the original poster.