\[f(x) = \sqrt{x - 5} - \frac{3}{\sqrt{4 - x}},\ \ \]
\[\left\{ \begin{matrix} x - 5 \geq 0 \\ 4 - x > 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\left\{ \begin{matrix} x \geq 5 \\ x < 4 \\ \end{matrix} \right.\ \]
\[\Longrightarrow D(f) = \varnothing.\]