  In this paper we study the scattering of non-radial solutions in the energy
space to coupled system of nonlinear Schr\"{o}dinger equations with
quadratic-type growth interactions in dimension five without the mass-resonance
condition. Our approach is based on the recent technique introduced by Dodson
and Murphy, which relies on an interaction Morawetz estimate. It is proved that
any solution below the ground states scatters in time.
