Answer
$\log_5\dfrac{x^{\frac{7}{3}}}{(x+5)^3}$
Work Step by Step
Using the properties of logarithms, the given expression, $
2\log_5x+\dfrac{1}{3}\log_5x-3\log_5(x+5)
,$ simplifies to
\begin{array}{l}\require{cancel}
\log_5 x^2+\log_5 x^{\frac{1}{3}}-\log_5 (x+5)^3
\\\\=
\log_5\dfrac{x^2\cdot x^\frac{1}{3}}{(x+5)^3}
\\\\=
\log_5\dfrac{x^{2+\frac{1}{3}}}{(x+5)^3}
\\\\=
\log_5\dfrac{x^{\frac{6}{3}+\frac{1}{3}}}{(x+5)^3}
\\\\=
\log_5\dfrac{x^{\frac{7}{3}}}{(x+5)^3}
.\end{array}
