5. Given that $D, F$ are points on the sides $A B, A C$ of $\triangle A B C$ respectively, and $A D: D B=C F: F A=2: 3$, connect $D F$ to intersect the extension of side $B C$ at point $E$, find $E F: F D$.
5. A line intersects $\triangle A B C$, and we have $\frac{C F}{F A} \cdot \frac{A D}{D B} \cdot \frac{B E}{E C}=\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{B E}{E C}=1$, so $\frac{B E}{E C}=\frac{9}{4}$, hence $\frac{B C}{C E}=\frac{5}{4}$. The line intersects $\triangle D B E$, and we have $\frac{E F}{F D} \cdot \frac{A D}{A B} \cdot \frac{B C}{C E}=\frac{E F}{F D} \cdot \frac{2}{5} \cdot \frac{5}{4}=1$, thus $E F: F D=2: 1$.