  We consider black strings in five dimensions and their description as a (4,0)
CFT. The CFT moduli space is described explicitly, including its subtle global
structure. BPS conditions and global symmetries determine the spectrum of
charged excitations, leading to an entropy formula for near-extreme black holes
in four dimensions with arbitrary charge vector. In the BPS limit, this formula
reduces to the quartic E(7,7) invariant. The prospects for a description of the
(4,0) theory as a solvable CFT are explored.
