Is it simple?

Algebra Level 3

Given \( x, y, z \) such that

\[\begin{array}{l r l} {\rm{If}} & x + y + z & = 1,\\ \quad & {x^2} + {y^2} + {z^2} & = 2,\\ \quad & {x^3} + {y^3} + {z^3} & = 3,\\ \end{array}\]

what is the value of

\[ x^5 + y^5 + z^5 \]

to 2 decimal places?

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