The ratio of the radii of two circles is $5:4$. What is the ratio of their respective areas?

Let the radii of the two circles be $r_1$ and $r_2$, such that $\frac{r_1}{r_2}=\frac{5}{4}$.
The area of a circle is calculated using the formula $A=\pi r^2$. Taking the ratio of their areas:

$$\frac{A_1}{A_2}=\frac{\pi r_1^2}{\pi r_2^2}={\left(\frac{r_1}{r_2}\right)}^2$$

$$\frac{A_1}{A_2}={\left(\frac{5}{4}\right)}^2=\frac{25}{16}$$

Therefore, the ratio of their areas is $25:16$.