Five, (20 points)
Solve the system of equations: $x, y, z \in \mathbf{R}^{+}$
$$
\left\{\begin{array}{l}
x^{2}+y^{2}+\sqrt{3} x y=20+8 \sqrt{3} \\
y^{2}+z^{2}=13 \\
z^{2}+x^{2}+x z=37
\end{array}\right.
$$

Find $(x, y, z)$.