Mathematical sequence

Trying to cheat on the Lenny Conundrum?

From 1 to 721: The difference is 720
720 = 6!

From 721 to 727 the difference is 6
6 = 3!

From 727 to 5767 the difference is 5040
5040 = 7!

From 5767 to 5791 the difference is 24
24 = 4!

From 5791 to 5792 the difference is 1
1 = 1!

Thus the pattern of differences is always a factorial.
6!, 3!, 7!, 4!, 1!...

Subtract 3! Form every next difference, but you add 7! If it gets to "0" or less than 0

So the sequence is

6!, 3!, 7!, 4!, 1!, 5!, 2!, 6!, 3!, …… which is repeating

So the next number is

5! = 5 x 4 x 3 x 2 x 1 = 120

= 5792 + 120

= 5912