  We obtain new non-extremal rotating black hole solutions in maximal
five-dimensional gauged supergravity. They are characterised by five
parameters, associated with the mass, the two angular momenta, and two
independently-specifiable charge parameters. Two of the three charges
associated with the U(1)^3 Cartan subgroup of the SO(6) gauge group are equal,
whilst the third can be independently specified. These new solutions generalise
all the previously-known rotating solutions in five-dimensional gauged
supergravity with independent angular momenta. They describe regular black
holes, provided the parameters lie in appropriate ranges so that naked
singularities and closed-timelike curves (CTCs) are avoided. We also construct
the BPS limit, and show that regular supersymmetric black holes or topological
solitons arise if the parameters are further restricted in an appropriate
manner.
