Answer
$\ln{\left(\frac{m^5}{n^3}\right)}$
Work Step by Step
Recall:
(1) $n\cdot \ln{a}=\ln{a^n}$
(2) $\ln{a}+\ln{b}=\ln{(ab)}$
(3) $\ln{a}-\ln{b} = \ln{\left(\frac{a}{b}\right)}$
Use rule (1) above to obtain:
\begin{align*}
5\ln{m}-3\ln{n}&=\ln{\left(m^5\right)}-\ln{\left(n^3\right)}\\
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
\ln{\left(m^5\right)} - \ln{(n^3)}&=\ln{\left(\frac{m^5}{n^3}\right)}
\end{align*}