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Baker showed that 10 of the 12 classes of Berge knots are obtained by surgeryon the minimally twisted 5-chain link. In this article we enumerate allhyperbolic knots in S^3 obtained by surgery on the minimally twisted 5 chainlink that realize the maximal known distances between slopes corresponding toexceptional (lens, lens), (lens, toroidal), (lens, Seifert fibred spaces)pairs. In light of Baker's work, the classification in this paper conjecturallyaccounts for 'most' hyperbolic knots in S^3 realizing the maximal distancebetween these exceptional pairs. All examples obtained in our classificationare realized by filling the magic manifold. The classification highlightsadditional examples not mentioned in Martelli and Petronio's survey of theexceptional fillings on the magic manifold. Of particular interest, is anexample of a knot with two lens space surgeries that is not obtained by fillingthe Berge manifold.

On hyperbolic knots in S^3 with exceptional surgeries at maximal distance