linear algebra - Do similar, non-diagonalizable matrices have the same eigenvalues?

To better explain, I have the matrix
$$\begin{bmatrix}3&2&0\\5&0&0\\k&b&-2\end{bmatrix}$$
where k is chosen to make the matrix non-diagonal. I have to find, if possible, a matrix with the same eigenvalues which is not similar to this one, but I can't seem to find it.
Is it only this particular case, or in general non-diagonalizable matrices that are not similar have different eigenvalues?

Thanks in advance.