We compactify M-theory on a Calabi-Yau manifold to five dimensions by
wrapping the membrane and fivebrane solitons of the eleven-dimensional
supergravity limit around Calabi-Yau two-cycles and four-cycles, resp
ectively. We identify the perturbative and non-perturbative BPS states
thus obtained with those of heterotic string theory compactified on K
3 x S-1. Quantum aspects of the five-dimensional theory are discussed.