  It has recently been shown that the uniqueness theorem for stationary black
holes cannot be extended to five dimensions. However, uniqueness is an
important assumption of the string theory black hole entropy calculations. This
paper partially justifies this assumption by proving two uniqueness theorems
for supersymmetric black holes in five dimensions. Some remarks concerning
general properties of non-supersymmetric higher dimensional black holes are
made. It is conjectured that there exist new families of stationary higher
dimensional black hole solutions with fewer symmetries than any known solution.
