We construct a new class of black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. These configurations are cohomogeneity-1, with two equal-magnitude angular momenta. In the generic case, they possess a non-vanishing magnetic potential at infinity with a boundary metric which is the product of time and a squashed three-dimensional sphere. Both extremal and non-extremal black holes are studied. The non-extremal black holes satisfying a certain relation between electric charge, angular momenta and magnitude of the magnetic potential at infinity do not trivialize in the limit of vanishing event horizon size, becoming particle-like (non-topological) solitonic configurations. Among the extremal black holes, we show the existence of a new oneparameter family of supersymmetric solutions, which bifurcate from a critical Gutowski-Reall configuration.11 Their basic properties have been discussed in a different context in [35], [36]. 12 In understanding the limiting-v behaviour, some useful hints are provided by the nutty-instanton toy model in Appendix A.13 However, for black strings, the Gregory-Laflamme instability [37] implies the existence of a critical periodicity of theψ-coordinate for a given value of the mass [38].