Identify the relevant triangle and points.

Consider $\triangle AFC$. Point $D$ is on side $AF$, and point $E$ is on side $AC$.

We are given $\frac{AD}{AF} = \frac{3}{5}$.
This means that $AD$ is 3 parts and $AF$ is 5 parts.
So, $DF = AF - AD = 5 \text{ parts} - 3 \text{ parts} = 2 \text{ parts}$.
Therefore, the ratio $\frac{AD}{DF} = \