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For this problem the eigen values are $5$, $-1$, $-1$ and the minimal polynomial is $x^2-4x-5$.

From eigenvectors, I can see this as diagonalizable.

The question specifically asks to determine it from the minimal polynomial. How do I determine it from the minimal polynomial?

Irregardless
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    https://math.stackexchange.com/questions/833759/minimal-polynomial-of-diagonalizable-matrix – B.Swan Aug 07 '17 at 22:57

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The minimal polynomial $x^2-4x-5=(x+1)(x-5) $ factors completely over $\mathbb R $ into distinct linear factors... This is equivalent to diagonalizability here.