In this paper we study the scalar geometries occurring in thedimen-sional reduction of minimal five-dimensional supergravityto three Eu-clidean dimensions, and find that these depend on whether onefirst re-duces over space or over time. In both cases the scalar manifold of thereduced theory is described as an eight-dimensional Lie groupL(the Iwa-sawa subgroup ofG2(2)) with a left-invariant para-quaternionic-K ̈ahlerstructure. We show that depending on whether one reduces first overspace or over time, the groupLis mapped to two different openL-orbitson the pseudo-Riemannian symmetric spaceG2(2)/(SL(2)·SL(2)). Thesetwo orbits are inequivalent in the sense that they are distinguished by theexistence of integrableL-invariant complex or para-complex structures.