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

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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