generators of alternating groups?

Question

Let $A_{5}$ be the alternating subgroup of the symmetric group $S_{5}$. Prove that $A_{5}$ is generated by the two elements $\{a=(123),b=(12345)\}$, or equivalently can we write the element $(234)$ as a composition of the two elements $a$ and $b$.

Answer 1

For the second question, note that $(123)^2(12345)=(145)$, and try repeating the process.