Answer
$\displaystyle \ln(\frac{x^{5}}{y^{2}})$
Work Step by Step
$ 5\ln x-2\ln y=\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\ln x^{5}-\ln y^{2}\quad $...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\displaystyle \ln(\frac{x^{5}}{y^{2}})$