1. **State the problem:** We have a transversal line $t$ crossing two horizontal lines $a$ (top) and $m$ (bottom), creating angles at the intersections. Given that angle 7 measures $113^\circ$, find the measure of angle 5. 2. **Recall important rules:** When a transversal crosses parallel lines, alternate interior angles are equal, and angles on a straight line sum to $180^\circ$. 3. **Analyze the bottom intersection:** Angles 5, 6, 7, and the unlabeled angle form a full circle ($360^\circ$). Also, angles 5 and 7 are alternate interior angles with angles 1 and 3 respectively. 4. **Use the straight line rule at the bottom intersection:** Angles 6 and 7 are adjacent and form a straight line, so $$\angle 6 + \angle 7 = 180^\circ.$$ Given $\angle 7 = 113^\circ$, then $$\angle 6 = 180^\circ - 113^\circ = 67^\circ.$$ 5. **Use vertical angles at the bottom intersection:** Angles 5 and 6 are vertical angles, so they are equal: $$\angle 5 = \angle 6 = 67^\circ.$$ **Final answer:** $$\boxed{67^\circ}$$