Suppose we have a permutation on the set {1,2,3,4,5} and we express it in the cycle notation as (2,5,3). I interpret this to mean that every time we apply the permutation, 2 gets sent to 5, 5 gets sent to 3 and 3 gets sent to 2. All other elements are mapped to themselves. Formally, I think it is equivalent to $\begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 1 & 5 & 2 & 4 & 3 \end{pmatrix}$. An equivalent expression is (2,3)(2,5). But if I were to have a consistent interpretation of the cycle notation, then this would mean 2 gets sent to 5 first, then 5 gets sent to itself. How is it indicated that 5 gets sent to 3?
Why am I being downvoted?