1. **State the problem:** We need to find the value of $x$ given two angles formed by a transversal intersecting two parallel lines. The angles are $(5x - 3)^\circ$ and $62^\circ$. 2. **Identify the relationship:** Since the lines are parallel and the angles are corresponding angles, they are equal. 3. **Set up the equation:** $$5x - 3 = 62$$ 4. **Solve for $x$:** Add 3 to both sides: $$5x = 62 + 3$$ $$5x = 65$$ Divide both sides by 5: $$x = \frac{65}{5}$$ $$x = 13$$ 5. **Conclusion:** The value of $x$ is 13.