In joint work with Jakob Glas, we prove upper bounds for the number of rational points on del Pezzo surfaces of degree ≤5 using a hyperplane section argument. Our work is valid over all global fields excluding characteristic 2 and 3. Over number fields our results are conditional on a hypothesis concerning the growth of the rank of elliptic curves in terms of the conductor. En passant we also produce new (unconditional) upper bounds for del Pezzo surfaces of degree five which admit a conic bundle structure.