It depends on the use of the car. The 5W designates the cold start viscosity and that should stay the same regardless of use.
It's the second number that can change. For normal day to day street use 5W20 is absolutely fine because the 4.6 3V and the 5.0 Coyote were built with tight tolerances.
I'd recommend running 5W30 on a higher mileage engine simply because those tolerances will be slightly looser. If you're mostly a cruiser and only an occasional racer, 5W30 would probably be OK.
Should you run 5W50? For street use I'd say it's unnecessary. For the drag strip it's also unnecessary because you're only running the engine at higher rpm in very short bursts. It probably IS needed is when road racing, where the engine does spend sustained periods at higher rpm, generating a lot of heat that'll thin the oil and compromise its film strength if its viscosity is too low to begin with. The Boss 302 was fitted with an oil cooler because of its higher revving nature, and that can be retrofitted to a Gen 1 Coyote if it's also modified to run past 7000rpm.
One item I'd highly recommend on any car that's frequently used for road racing is a higher capacity oil pan with extra baffles and trap doors for improved oil control. This can literally be the difference between finishing the race with a perfectly running engine or grenading it due to oil pressure drops during hard cornering causing oil starvation of the rod/main bearings.
