  We consider rotating black hole solutions in five-dimensional
Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and
a generic value of the Chern-Simons coupling constant $\lambda$. Using both
analytical and numerical techniques, we focus on cohomogeneity-1
configurations, with two equal-magnitude angular momenta, which approach at
infinity a globally AdS background. We find that the generic solutions share a
number of basic properties with the known Cvetic, L\"u and Pope black holes
which have $\lambda=1$. New features occur as well, for example, when the
Chern-Simons coupling constant exceeds a critical value, the solutions are no
longer uniquely determined by their global charges. Moreover, the black holes
possess radial excitations which can be labelled by the node number of the
magnetic gauge potential function. Solutions with small values of $\lambda$
possess other distinct features. For instance, the extremal black holes there
form two disconnected branches, while not all near-horizon solutions are
associated with global solutions.
