Interesting indeed.
I notice that:
5^1 mod 7 = 5 but is less than 7 so we can't use that
5^2 mod 7 = 4 so we have 4 "repeat" results
5^3 mod 7 = 6 so we have 6 "repeat" results
5^4 mod 7 = 2 so we have 2 "repeat" results
5^5 mod 7 = 3 so we have 3 "repeat" results
5^6 mod 7 = 1 so we have only one "repeat" result
5^7 mod 7 = 5 and it repeats from there
