Bash me up please!

Algebra Level 4

\[\large\large{ \begin{cases} a+b+c=1 \\ a^2+b^2+c^2 = 2 \\ a^3 + b^3+c^3 = 3 \\ \end{cases} } \]

Find \(\large\large a^5 + b^5 + c^5 \).

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