We prove L1 → L∞ dispersive estimates with a logarithmic loss of derivatives for the Schrödinger group eit(−Δ+V) for a class of real-valued potentials V ∈ C(n−3)/2(ℛn), V(x) = O(⟨x⟩−δ), where n = 4, 5, δ > 3 if n = 4 and δ > 5 if n = 5.