  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.
