3. (GDR 1) Knowing that the system 
\[ \begin{aligned} x+y+z & =3, \\ x^{3}+y^{3}+z^{3} & =15, \\ x^{4}+y^{4}+z^{4} & =35, \end{aligned} \]
has a real solution \(x, y, z\) for which \(x^{2}+y^{2}+z^{2}<10\), find the value of \(x^{5}+y^{5}+z^{5}\) for that solution.