We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N = 1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor supermultiplet is described in superspace for the first time. Open Access, © 2014 The Authors.