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

$$f = \displaystyle\left(\begin{array}{cccccc} 1 &2 &3 &4 &5 &6 \cr 5 &2 &3 &6 &1 &4 \cr \end{array}\right)$$
(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 $f^{5}$.