$A^5 = \begin{bmatrix} 32 & 100000 \\ 0 & 3125 \end{bmatrix}$. The determinant of $A$ is $M$. The closest integer of summing up the four entries in $A$ is $N = \mathrm{round}(A_{11} + A_{12} + A_{21} + A_{22})$. What is the value of mod($M + N \times 13$, 5), where mod(.) is the modulo operation.