1. **State the problem:** Find the equation of the line passing through the point $(5, 10)$ and perpendicular to the line $x = -3$. 2. **Understand the given line:** The line $x = -3$ is a vertical line where all points have $x$-coordinate $-3$. 3. **Perpendicular line rule:** A line perpendicular to a vertical line is a horizontal line. 4. **Equation of a horizontal line:** A horizontal line has the form $y = c$, where $c$ is a constant. 5. **Find $c$ using the point $(5, 10)$:** Since the line passes through $(5, 10)$, the $y$-coordinate is $10$, so $c = 10$. 6. **Final equation:** The line perpendicular to $x = -3$ passing through $(5, 10)$ is $$y = 10.$$