Hooke’s law states that extension x is proportional to force F, provided that the limit of proportionality is not exceeded, i.e. x ∝ F or x = kF where k is a constant.
When x = 2 mm, F = 250 N, thus 2 = k(250),
from which, constant k = 2/250 = 1/125
i.e. 5 = (1/125)F
from which, force F = 5(125) = 625 N
Thus to stretch the wire 5 mm a force of 625 N is required.