  We construct new non-extremal rotating black hole solutions in SO(6) gauged
five-dimensional supergravity. Our solutions are the first such examples in
which the two rotation parameters are independently specifiable, rather than
being set equal. The black holes carry charges for all three of the gauge
fields in the U(1)^3 subgroup of SO(6), albeit with only one independent charge
parameter. We discuss the BPS limits, showing in particular that these include
the first examples of regular supersymmetric black holes with independent
angular momenta in gauged supergravity. We also find non-singular BPS solitons.
Finally, we obtain another independent class of new rotating non-extremal black
hole solutions with just one non-vanishing rotation parameter, and one
non-vanishing charge.
