5. In a village, two houses $A$ and $B$ stand along a straight road, 50 meters apart from each other. At what point on the road should a well be built so that the sum of the distances from the well to the houses is minimized?
$\triangle$ If we act fairly, we should build the well in the middle between the houses: then the distance to each house will be 25 meters, and in total 50. However, from the point of view of the problem's condition, any point $X$ on the road segment between $A$ and $B$ is equally good, since the segments $A X$ and $X B$ in total make up 50 meters. (For example, if the well is built 10 meters from $A$, the distances will be 10 and 40 meters, which is 50 in total.) $\triangleleft$