Let $A$ be the matrix $\left(\begin{array}{ccccc} 0 & -1 & 2 & -2 & -1 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & -1 & 1 & 0 \end{array}\right)$ and $u$ the endomorphism canonically associated with $A$.
Determine the partition $\sigma$ of the integer 5 associated with $u$ and give the matrix $N_\sigma$.