  We study 5d supersymmetric black holes which descend from strings of generic
$\mathcal{N}=(1,0)$ supergravity in 6d. These strings have an F-theory
realization in 6d as D3 branes wrapping smooth genus $g$ curves in the base of
elliptic 3-folds. They enjoy $(0,4)$ worldsheet supersymmetry with an extra
$SU(2)_L$ current algebra at level $g$ realized on the left-movers. When the
smooth curves degenerate they lead to multi-string branches and we find that
the microscopic worldsheet theory flows in the IR to disconnected 2d CFTs
having different central charges. The single string sector is the one with
maximal central charge, which when wrapped on a circle, leads to a 5d spinning
BPS black hole whose horizon volume agrees with the leading entropy prediction
from the Cardy formula. However, we find new phenomena where this branch meets
other branches of the CFT. These include multi-string configurations which have
no bound states in 6 dimensions but are bound through KK momenta when wrapping
a circle, as well as loci where the curves degenerate to spheres. These loci
lead to black hole configurations which can have total angular momentum
relative to a Taub-Nut center satisfying $J^2 > M^3$ and whose number of
states, though exponentially large, grows much slower than those of the large
spinning black hole.
