Find all $6 \times 6$ matrices knowing the trace and $A^3-6A^2+5A=0$

Question

I have to find all matrices $A$ that satisfy:

• Trace of matrix $A$ is $17$
• $A^3-6A^2+5A=0$

I have calculated characteristic polynomial $X(X-1)^2(X-5)^3$ and minimal polynomial $X(X-1)(X-5)$, so eigenvalues are $0$, $1$ and $5$. Diagonal matrices with these values answer the question. But how to find all matrices?