Let $ p \in \mathbb {Z}[X] $ and of fifth degree with only the terms for $x^5$, $x^4$ and $x^3$ known, the terms for $x^2$, $x$ and $1$ are not known. $$ p=x^5  5x^4  35x^3 + \cdots $$ The ( five ) roots of $p $ form an arithmetic sequence. Find the roots of $p $.
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