  Supersymmetric black holes in five-dimensional gauged supergravity must
necessarily be rotating, and so in order to study the passage to black holes
away from supersymmetry, it is of great interest to obtain non-extremal black
holes that again have non-zero rotation. In this paper we find a simple
framework for describing non-extremal rotating black holes in five-dimensional
gauged supergravities. Using this framework, we are able to construct a new
solution, describing the general single-charge solution of N=2 gauged
supergravity, with arbitrary values for the two rotation parameters.
Previously-obtained solutions with two or three equal charges also assume a
much simpler form in the new framework, as also does the general solution with
three unequal charges in ungauged N=2 supergravity. We discuss the
thermodynamics and BPS limit of the new single-charge solutions, and we discuss
the separability of the Hamilton-Jacobi and Klein-Gordan equations in these
backgrounds.
