Building on the covariant supergraph techniques in 4D N = 2 harmonic superspace, we develop a manifestly 5D N = 1 supersymmetric and gauge covariant formalism to compute the one-loop effective action for a hypermultiplet coupled to a background vector multiplet. As a simple application, we demonstrate the generation of a supersymmetric Chern-Simons action at the quantum level, both in the Coulomb and the non-Abelian phases. These superfield results are in agreement with the earlier component considerations of Seiberg et al. Our analysis suggests that similar calculations in terms of hybrid 4D superfields or within the 5D projective superspace approach may allow one to extract suitable formulations for the non-Abelian 5D supersymmetric Chern-Simons theory. (c) 2006 Elsevier B.V. All rights reserved.