(5) The minimum value of the function $f(x)=\sqrt{x^{2}+9}+\sqrt{x^{2}-8 x+17}$ is
(5) $4 \sqrt{2}$ Hint: Utilize
$$
\sqrt{a^{2}+b^{2}}+\sqrt{c^{2}+d^{2}} \geqslant \sqrt{(a+c)^{2}+(b+d)^{2}},
$$

then
$$
\begin{aligned}
f(x) & =\sqrt{x^{2}+3^{2}}+\sqrt{(4-x)^{2}+1^{2}} \\
& \geqslant \sqrt{4^{2}+4^{2}}=4 \sqrt{2}.
\end{aligned}
$$