Let $D$ be the $6 \times 6$ diagonal matrix with diagonal entries $5$.
Then all the $6 \times 6$ complex matrices which are diagonalizable to $D$ are conjugate to $D$ and hence to each other.
So I should find those matrices which aren't diagonalizable to $D$ but have same characteristic equation.
I think of those matrices whose all diagonal elements are $5$ but Geometric multiplicity $\neq$ Algebraic multiplicity for $5$. But still not getting any concrete idea.
What is the general way to approach?