Question: Use Cayley-Hamilton theorem to express $A^5-4A^4-7A^3+11A^2-A-10I$, where $A= \begin{pmatrix}1&4\\2&3\end{pmatrix}$
Attempt: I only know how to get the characteristic polynomial equation which is $\lambda^2-4\lambda -5$ for that matrix. By definition $A^2-4A-5=0$. But where does that 5 degree polynomial come from?