Jordan Form Over Reals with Knowledge of Eigenvalues

Question

Say I have a matrix $A$ that I know is 5x5 with the only eigenvalues $\lambda_1 = 2$, $\lambda_2 = 1 + i$, and $\lambda_3 = 1-i$. I'm trying to list all of the Jordan Forms this matrix can have, over the reals. So I know that the characteristic polynomial is either $(x-2)^3(x^2-2x+2)$ or $(x-2)(x^2-2x+2)^2$. I know all the forms associated with the first polynomial, but I'm a bit confused about the second form. I know one of the forms associated with $(x-2)(x^2-2x+2)^2$ is, but since the minimal polynomial could be either $(x-2)(x^2-2x+2)^2$ or $(x-2)(x^2-2x+2)$, so it should have two different forms, so my question is, which minimal polynomial corresponds to this form and what is the other form/how do you find it? \begin{pmatrix} 2&0&0&0&0\\ 0&1&1&0&0\\ 0&-1&1&0&0\\ 0&0&0&1&1\\ 0&0&0&-1&1\\ \end{pmatrix}