a) 5 meters
Start with the extremes, and work backwards.
Straight ahead (OK, may 1' turn) would be 23 + 14 = 37. Not one of the options.
Straight back (180' 'turn') would be 23 - 14 = 9, also not an option, but as a minimum displacement it also eliminates 5 meters as an option.
Therefore, all of the others (10, 15, 20, 25) are possible, depending on the turn angle. ONLY a) 5 meters is NOT possible of the choices.
Since none of the directions of motion are given, any answer except a.) is a possible outcome or the change in displacement.
The change in displacement would depend only on the angle at which the runner turns after running the first
For example if the runner turns
At the same time,
The rest of the choices are all possible because his longest possible distance is
There is an example of negative displacement here: