We extend belief revision theory from propositional logic to the modal logic S5. Syntactically, we formulate three new postulates capturing the idea of minimal change in the presence of modalities. Semantically, we investigate revision operations defined from set pseudo-distances: distances between sets of points that may violate the triangle-inequality. Our first contribution is the identification of axioms on pseudo-distances guaranteeing that the modal postulates hold. The second contribution is the evaluation of three pseudo-distances from the literature: we show that only one of them satisfies all axioms. The third contribution applies revision based on that pseudo-distance in order to revisit a major criticism of AGM revision operations, namely that the revisions of $p \land q$ and $p \land p \to q$ are identical. We show that the problem disappears if instead of material implication we use the modal operator of strict implication that can be defined in S5.