Multi-angle five-brane intersections

We find new solutions of IIA supergravity which have the interpretation of intersecting NS-5-branes at Sp(2)-angles on a string preserving at least 3/32 of supersymmetry. We show that the relative position of every pair of NS-5-branes involved in the superposition is determined by four angles. In addition we explore the related configurations in IIB strings and M-theory.