The diffusivities of long n-alkanes in ZSM-5 have been measured by quasi-elastic neutron scattering (QENS). Self-diffusion coefficients and activation energies for chains up to C-14 have been obtained. Reasonable agreement is observed with single-crystal membrane experiments, except for C-6, but large discrepancies are found with the zero-length column (ZLC) method. The diffusivities predicted by a hierarchical simulation diverge from those measured by QENS after C-6, although the activation energies for diffusion are comparable. The discrepancy with MD simulations is larger. QENS results show that diffusion of branched alkanes is much more restricted than the one of linear alkanes in this structure.