Consider the system of nonlinear equations:
\[ \begin{cases} 
x + y + z = 3 \\
xy + yz + zx = 4 \\
xyz = 5 
\end{cases} \]
Find the sum of the squares of the roots of the polynomial whose roots are \(x, y,\) and \(z\). Let's think step by step and output the final answer within \boxed{}.
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