Toroidal Dehn fillings on hyperbolic 3-manifolds

We determine all hyperbolic 3-manifolds M admitting two toroidal Dehn fillings at distance 4 or 5. We show that if M is a hyperbolic 3manifold with a torus boundary component T0, and r, s are two slopes on T0 with ∆(r, s) = 4 or 5 such that M(r) and M(s) both contain an essential torus, then M is either one of 14 specific manifolds Mi, or obtained from M1, M2, M3 or M14 by attaching a solid torus to ∂Mi −T0. All the manifolds Mi are hyperbolic, and we show that only the first three can be embedded into S. As a consequence, this leads to a complete classification of all hyperbolic knots in S admitting two toroidal surgeries with distance at least 4.