Answer
$\ln 5$
Work Step by Step
When x approaches the value $5$ from the right side, $x\rightarrow 5^{+},$
$x\rightarrow 5,$
$x-4\rightarrow 1$,
$\sqrt{x-4}\rightarrow 1$,
$\displaystyle \frac{x}{\sqrt{x-4}}\rightarrow\frac{5}{1}=5$,
$\displaystyle \ln\left(\frac{x}{\sqrt{x-4}}\right)\rightarrow\ln 5$
