Final answer:
The bicyclist's displacement is 5 km east since the north and south displacements cancel each other out, and there is a remaining 5 km displacement in the east direction.
Step-by-step explanation:
The question involves calculating the displacement of a bicyclist who travels in different directions. Displacement is a vector quantity that represents the shortest distance from the initial to the final position and is direction-sensitive. In this case, the bicyclist travels 25 km east and 20 km west, which effectively means a net displacement of 5 km east. Additionally, the cyclist travels 15 km south and then 15 km north, which cancel each other out resulting in no net displacement in the north-south direction. Therefore, the cyclist's total displacement is only in the east direction, which is the same as the net displacement of 5 km east.