A hydrodynamic scattering treatment of interacting polymer chains is extended to obtain the five-point chain-chain-chain-chain-chain hydrodynamic interaction tensor. The tensor is used to calculate the second-order concentration correction to the self-diffusion coefficient of a polymer in solution. The self-similarity assumption of the hydrodynamic scaling model of polymer dynamics is tested against these calculations. (C) 2004 Wiley Periodicals, Inc.