  We find and study supergravity BPS bound states of five-dimensional spinning
black holes in asymptotically flat spacetime. These solutions follow from
multi-string solutions in six-dimensional minimal supergravity and can be
uplifted to F-theory or M-theory. We analyze the regularity conditions and work
out the example of a bound state of two black holes in detail. The bound state
is supported by fluxes through nontrivial topologies exterior to the horizons
and KK momentum. Furthermore, we determine the entropy and compare with other
macroscopic BPS solutions.
