The matrix \begin{equation*} P= \begin{bmatrix} 0&1&0&0&0\\ 0&0&0&1&0\\ 1&0&0&0&0\\ 0&0&0&0&1\\ 0&0&1&0&0 \end{bmatrix} \end{equation*} is unitary as can be easily checked. Notice that it is just a rearrangement of the columns of the $5\times 5$ identity matrix, $I_5$ (Definition IM).
An interesting exercise is to build another $5\times 5$ unitary matrix, $R$, using a different rearrangement of the columns of $I_5$. Then form the product $PR$. This will be another unitary matrix (Exercise MINM.T10). If you were to build all $5!=5\times 4\times 3\times 2\times 1=120$ matrices of this type you would have a set that remains closed under matrix multiplication. It is an example of another algebraic structure known as a group since together the set and the one operation (matrix multiplication here) is closed, associative, has an identity ($I_5$), and inverses (Theorem UMI). Notice though that the operation in this group is not commutative!