4. If $x, y, z \in \mathbf{R}_{+}$, satisfy $x y+y z+z x=1$, then the maximum value of the function $f(x, y, z)=\sqrt{x y+5}+\sqrt{y z+5}+\sqrt{z x+5}$ is $\qquad$ .
By the Cauchy-Schwarz inequality, we have $(\sqrt{x y+5}+\sqrt{y z+5}+\sqrt{z x+5})^{2}$ $\leqslant(1+1+1)(x y+5+y z+5+z x+5)=48 \Rightarrow f(x, y, z) \leqslant 4 \sqrt{3}$, equality holds when $x=y=z=\frac{\sqrt{3}}{3}$. Therefore, the maximum value of the function $f(x, y, z)$ is $4 \sqrt{3}$.