1. **State the problem:** Find the equation of the line passing through the point $(5,3)$ with an undefined slope. 2. **Recall the concept:** A line with an undefined slope is a vertical line. 3. **Formula and rule:** Vertical lines have equations of the form $$x = a$$ where $a$ is the $x$-coordinate of any point on the line. 4. **Apply the rule:** Since the line passes through $(5,3)$, the $x$-coordinate is $5$. 5. **Write the equation:** The equation of the line is $$x = 5$$. This means the line is vertical and crosses the $x$-axis at $5$.