Remember that the boiling points of alkanes increase with increasing number of carbons. This is because the intermolecular attractive forces, although individually weak, become cumulatively more significant as the number of atoms and electrons in the molecule increases.
So the hydrocarbon with less number of carbons will have the lowest boiling point, thus wil be removed first from the distillation tower.
So on the distillation tower the compounds will be distilled in this order:
I - C2H6
II - C8H18
III - C14H30
IV - C22H40
V - C35H72