If you try to imagine a walkway has a total of 60 yards starting from the first streetlight down to the last streetlight. Knowing that there are a total of five streetlights all in all, that means there are only 3 left to space evenly between the first and the last streetlight. Consequently, there would be four spaces all in all. Please see the picture so that you would understand better.
That means there are 4 evenly spaced lengths measuring to x yards. Therefore,
x = 60/4 = 15 yards
The distance between each light is 15 yards.