1. **State the problem:** Given two parallel lines $\ell \parallel m$ cut by a transversal, prove that angles $\angle 3$ and $\angle 5$ are supplementary. 2. **Recall the relevant property:** When two parallel lines are cut by a transversal, consecutive interior angles (also called same-side interior angles) are supplementary. 3. **Identify the angles:** $\angle 3$ and $\angle 5$ lie on the same side of the transversal and between the two parallel lines $\ell$ and $m$. 4. **Apply the Consecutive Interior Angles Theorem:** This theorem states that if two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary, meaning their measures add up to $180^\circ$. 5. **Write the equation:** $$ \angle 3 + \angle 5 = 180^\circ $$ 6. **Conclusion:** Therefore, $\angle 3$ and $\angle 5$ are supplementary by the Consecutive Interior Angles Theorem. **Final answer:** $\angle 3$ and $\angle 5$ are supplementary because $\ell \parallel m$ and the transversal creates consecutive interior angles.