1. The problem gives us two points: Laurie at $(-5,30)$ and Anne at $(23,9)$, and mentions a fountain halfway between them. 2. To find the fountain's coordinates, we calculate the midpoint of the segment joining Laurie's and Anne's positions. 3. The midpoint formula is $$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ where $(x_1,y_1) = (-5,30)$ and $(x_2,y_2) = (23,9)$. 4. Calculate the midpoint $x$-coordinate: $$\frac{-5 + 23}{2} = \frac{18}{2} = 9$$. 5. Calculate the midpoint $y$-coordinate: $$\frac{30 + 9}{2} = \frac{39}{2} = 19.5$$. 6. Thus, the fountain is located at the point $(9,19.5)$. 7. The problem also provides Anne's speed as $5$ km/h but does not request further calculations involving speed. Final answer: The fountain is at $\boxed{(9,19.5)}$.