#### Answer

$\color{blue}{\dfrac{5x}{9y^5}}$

#### Work Step by Step

Use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}=\frac{ad}{bc}$ to obtain:
$\require{cancel}
\\\frac{2x^2}{3y^4} \div \frac{6xy}{5}
\\=\frac{2x^2}{3y^4} \cdot \frac{5}{6xy}
\\=\frac{\cancel{2}\cancel{x^2}x}{3y^4} \cdot \frac{5}{\cancel{6}3\cancel{x}y}
\\=\frac{x}{3y^4} \cdot \frac{5}{3y}
\\=\frac{x(5)}{(3y^4)(3y)}
\\=\color{blue}{\frac{5x}{9y^5}}$