Algebra: A Combined Approach (4th Edition)

$3\log_{5}x-5\log_{5}y=\log_{5}\dfrac{x^{3}}{y^{5}}$
$3\log_{5}x-5\log_{5}y$ Take the coefficients $3$ and $5$ inside their respective logarithms as exponents: $3\log_{5}x-5\log_{5}y=\log_{5}x^{3}-\log_{5}y^{5}=...$ Combine $\log_{5}x^{3}-\log_{5}y^{5}$ as the $\log$ of a division: $...=\log_{5}\dfrac{x^{3}}{y^{5}}$