Answer
$m\angle5 = 108^{\circ}$
Work Step by Step
Postulate 11 says that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Since we are given that lines l and m are parallel, and $\angle1$ and $\angle5$ are corresponding angles, we know that $\angle1$ and $\angle5$ are congruent. Since $\angle1 = 108^{\circ}$, $\angle5$ must also be $108^{\circ}$.
