25. The range of the function $f(x)=\frac{\sqrt{x}+4-3}{x-5}$ is ( ).
(A) $\left(0, \frac{1}{3}\right]$
(B) $(-\infty, 0) \cup(0, \infty)$
(C) $\left(0, \frac{1}{6}\right) \cup\left(\frac{1}{6}, \frac{1}{3}\right]$
(D) $(0, \infty)$
(E) *
25. (C)

Let $z=x-5$. Then
$$
\begin{array}{l}
f(x)=\frac{\sqrt{x+4}-3}{x-5}=\frac{\sqrt{z+9}-3}{z}=\frac{1}{\sqrt{z+9}+3} . \\
\because z+9 \geqslant 0, \text { and } z \neq 0 . \\
\therefore \sqrt{z+9}+3 \geqslant 3 . \text { and } \sqrt{z+9}+3 \neq 6 . \\
\therefore 0 \leqslant \frac{1}{\sqrt{z+9}+3} \leqslant \frac{1}{3} \text { and } \frac{1}{\sqrt{z+9}+3} \neq \frac{1}{6} .
\end{array}
$$