  We discuss the relation between solutions admitting Killing spinors of
minimal supergravities in five dimensions and four dimensional complex
geometries. In the ungauged case (vanishing cosmological constant \Lambda=0)
the solutions are determined in terms of a hyper-Kahler base space; in the
gauged case (\Lambda<0) the complex geometry is Kahler; in the de Sitter case
(\Lambda>0) the complex geometry is hyper-Kahler with torsion (HKT). In the
latter case some details of the derivation are given. The method for
constructing explicit solutions is discussed in each case.
