  We consider the nonlinear Schr\"odinger equation in three space dimensions
with combined focusing cubic and defocusing quintic nonlinearity. This problem
was considered previously by Killip, Oh, Pocovnicu, and Visan, who proved
scattering for the whole region of the mass/energy plane where the virial
quantity is guaranteed to be positive. In this paper we prove scattering in a
larger region where the virial quantity is no longer guaranteed to be sign
definite.
