The formula for percentage increase is:
% increase = ΔPopulation/Population of base year * 100
In this problem, let x be the population of the base year. Hence, after 5 years, the population becomes 2x. Then, consequently, after 10 years, the population doubles to 4x. So, the ΔPopulation = 4x - x = 3x. Therefore,
% increase = x/3x * 100 = 33%