Matrices and Determinants: JEE Main 2021 Mathematics question

Let I be an identity matrix of order 2 $\times$ 2 and P = $\left[ {\matrix{ 2 & { - 1} \cr 5 & { - 3} \cr } } \right]$. Then the value of n$\in$N for which P^n = 5I $-$ 8P is equal to ____________.