Answer
$$\frac{a^3}{b^3}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{a^5}{b^4}\div \frac{a^2}{b} \\ \frac{a^5}{b^4}\times \frac{b}{a^2}\\ \frac{a^5b}{b^4a^2}\\ \frac{a^3}{b^3}$$