The effective action of N = 2 supersymmetric five-dimensional supergravity arising from compactifications of M-theory on Calabi-Yau threefolds receives non-perturbative corrections from wrapped euclidean membranes and fivebranes. These contributions can be interpreted as instanton corrections in the five-dimensional field theory. Focusing on the universal hypermultiplet, a solution of this type is presented and the instanton action is calculated, generalizing previous results involving membrane instantons. The instanton action is not a sum of membrane and fivebrane contributions: it has the form reminiscent of non-threshold bound states.