He has 3/5 m to use and uses 1/3 for his art project.
He uses, therefore, (1/3) * (3/5) = 1/5 for his art project and has 3/5 - 1/5 = (2/5)m remaining
You could also do it this way: since he uses 1/3 he must have 2/3 left, that is (2/3) * (3/5) = (2/5) m