  We give a unified description of all BPS states of M-theory compactified on
$T^5$ in terms of the five-brane. We compute the mass spectrum and degeneracies
and find that the $SO(5,5,Z)$ U-duality symmetry naturally arises as a
T-duality by assuming that the world-volume theory of the five-brane itself is
described by a string theory. We also consider the compactification on $S^1/Z_2
\times T^4$, and give a new explanation for its correspondence with heterotic
string theory by exhibiting its dual equivalence to M-theory on $K3\times S^1$.
