Klein bottle and toroidal Dehn fillings at distance 5

Abstract

We determine all hyperbolic 3-manifolds M such that M./ contains a Klein bottle, M./ contains an essential torus, and1.; / D 5. As a corollary, we prove that if a hyperbolic 3-manifold M has two slopes and on its boundary torus such that M./ is a lens space containing a Klein bottle and M./ is toroidal, then1.; / 4.