$\displaystyle \sigma =(135)(24) \ \text{and} \ \tau=(15)(23)$
$\displaystyle \sigma^2=(153)$
$\displaystyle \sigma\tau=(2534)$
$\displaystyle \tau\sigma=(1243)$
$\displaystyle \tau^2\sigma=(135)(24)$
Good?
looks good to me, assuming στ means do tau first, then sigma.
because one might have permutation groups that affect more than 9 elements, it is customary to leave spaces between the elements like so:
(1 3 5)(2 4)....this allows one to use numbers of more than one digit (some people use commas, which is ok, too).