In #5, each number is the sum of the two numbers that preceded it (with an implied zero before the first 1)
0, 1, 1, 2, 3, 5, 8, 13, 21, 34 (I don't know what S6 means, I just gave you the next number in the series.)
In #6, each number is the sum of 5 plus the number that preceded it.
1, 6, 11, 16, 21, 26, 31