Let $f$ be a permutation on the set $\lbrace 1, 2, 3, 4, 5, 6, 7 \rbrace$, defined as follows

$$f = ( 3\,1\,6 ) ( 1\,4\,5\,2 )$$
(a) Write the permutation $f^{5}$ as a product of disjoint cycles, separated by commas (e.g. $( 1, 2 ), ( 3, 4, 5 ), \ldots$ ).
Do not include 1-cycles (e.g. $(2)$ ) in your answer.

$f^{5} =$

(b) Determine the order of $f^{5}$.

Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so $(1,3)(1,2)=(1,2,3)$ not $(1,3,2)$.