Answer
$log_5(\frac{5^{1/3}}{m^{1/3}})$ or $log_5(\sqrt[3] {\frac{5}{m}})$
Work Step by Step
$-\frac{2}{3}log_5(5m^2)+\frac{1}{2}log_5(25m^2)=log_5(5m^2)^{-2/3}+log_5(5m)=log_5(5^{1/3}m^{-1/3})=log_5(\frac{5^{1/3}}{m^{1/3}})=log_5(\sqrt[3] {\frac{5}{m}})$