Since 4 isn't a commonly competed level they don't test mobility skills to go to 5 or need a mobility score.
5 to 6, I don't think we've ever formally tested the skills (so i don't know what they are, except a backdrop pullover to stomach).
But the routines are:
Trampoline-
4: Straddle jump
seatdrop
half turn to seat
front drop
return to feet
tuck jump
jump full twist
pike jump
back drop
return to feet.
5: Back drop
pullover
straddle jump
front drop
seat drop
half turn to feet
pike jump
jump half turn
tuck jump
front tuck.
Double mini:
(2 of 3 options)
4: Mounter tuck jump dismount straddle jump
spotter jump full turn dismount straddle jump
spotter tuck jump dismount jump full turn
5: Mounter straddle jump dismount pike jump
spotter tuck jump dismount front tuck
spotter pike jump dismount front pike
Tumbling:
4: Power hurdle roundoff 1 BHS
power hurdle roundoff 2 BHS
5: Power hurdle roundoff 2 BHS
Running roundoff 4 BHS