\[\begin{cases} &x &+ &y&+ &z&=&1 \\ &x^2&+&y^2&+&z^2&=&3 \\ &x^3&+&y^3&+&z^3&=&7 \end{cases} \]

If \(x,y\) and \(z\) satisfy the values of the system of equations above, find the value of \(x^5 + y^5 + z^5 \).

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