Permutation Groups · Hard problem

$D_5$, the symmetries of a regular pentagon, has order $10$ and is generated by a rotation $r$ of order $5$ and a reflection $s$ of order $2$. Under the left regular representation (Cayley's theorem) embedding $D_5$ into $S_{10}$, the permutation $\lambda_s$ (left multiplication by $s$) decomposes into disjoint $2$-cycles. How many $2$-cycles does it have?