  We consider 5D Einstein-Maxwell-dilaton (EMd) gravity in spacetimes with
three commuting Killing vectors: one timelike and two spacelike Killing
vectors, one of which is hypersurface-orthogonal. Assuming a special ansatz for
the Maxwell field we show that the 2-dimensional reduced EMd equations are
completely integrable. We also develop a solution generating method for
explicit construction of exact EMd solutions from known exact solutions of 5D
vacuum Einstein equations with considered symmetries. We derive explicitly the
rotating dipole black ring solutions as a particular application of the
solution generating method.
