  We consider a quintic Hartree equation for a random field, which describes
the temporal evolution of a infinitely many fermions, considering a three body
interaction. We show a scattering result around a non-localised equilibria of
the equation, for high dimensions $d\geq 4$. The Hartree equation for random
variables was introduced by Anne-Sophie de Suzzoni but only for a two body
interaction, that leads to a cubic Hartree equation for random variables.
Scattering results for the cubic Hartree equation have been shown by Charles
Collot and Anne-Sophie de Suzzoni, and we extend those results to the quintic
Hartree equation. We consider a large range of potentials that includes the
Dirac delta.
