  We construct the general solution for non-extremal charged rotating black
holes in five-dimensional minimal gauged supergravity. They are characterised
by four non-trivial parameters, namely the mass, the charge, and the two
independent rotation parameters. The metrics in general describe regular
rotating black holes, providing the parameters lie in appropriate ranges so
that naked singularities and closed timelike curves (CTC's) are avoided. We
calculate the conserved energy, angular momenta and charge for the solutions,
and show how supersymmetric solutions arise in a BPS limit. These have naked
CTC's in general, but for special choices of the parameters we obtain new
regular supersymmetric black holes or smooth topological solitons.
