Furthermore, for simplicity, we focus on the single black hole case, that is, the event horizon is connected. Then, we note that in five-dimensional EMCS theory the Cveti[č]{}-Youm black hole solution with equal charges [@CY96] appears to be the most general such solutions that describe an asymptotically flat, stationary charged rotating black hole with spherical horizon topology, characterized by four conserved charges, i.e., the mass, two independent angular momenta, and electric charge, and that encompass the known asymptotically flat, spherical black hole solutions in a subclass of EMCS theory, such as the Myers-Perry solution [@Myers:1986un], in a certain limit. Thus, we wish to show the following theorem.

[**Theorem.**]{} [*Consider, in five-dimensional Einstein-Maxwell-Chern-Simons theory \[given by eq. (\[action\]) below\], a stationary charged rotating black hole with finite temperature that is regular on and outside the event horizon and asymptotically flat in the standard sense with spherical spatial infinity. If (1) the black hole spacetime admits, besides the stationary Killing vector field, two mutually commuting axial Killing vector fields so that the isometry group is ${\Bbb R}\times U(1)\times U(1)$ and (2) the topology of the horizon cross-sections is spherical, ${\rm S^3}$, and the topology of the black hole exterior region is ${\Bbb 