Answer
Diverges
Work Step by Step
\begin{aligned}
\int_{5}^{6} \frac{d x}{(x-5)^{3 / 2}} &=\lim _{R \rightarrow 5} \int_{R}^{6} \frac{d x}{(x-5)^{3 / 2}} \\
&=\lim _{R \rightarrow 5}\left.\frac{(x-5)^{(-1 / 2)}}{-1 / 2}\right|_{R} ^{6} \\
&=\lim _{R \rightarrow 5} \left(\frac{2}{(R-5)^{(1 / 2)}}-2 \right)\\
&=\infty \end{aligned}
Then integral diverges.
