Permutated Peculiar Powers

Algebra Level 5

Given that the complex numbers \(x,y,z\) satisfy the equations: \[ \begin{eqnarray} x + y + z & = & 5 \\ x^3 + y^3 + z^3 & = & -19 \\ x^5 + y^5 + z^5 & = & -235, \\ \end{eqnarray} \]

what is the value of \(x^7 + y^7 + z^7 \)?

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