  Recently, an extension to the Parameterized Post-Newtonian (PPN) formalism
has been proposed. This formalism, the Parameterized
Post-Newtonian-Vainshteinian (PPNV) formalism, is well suited to theories which
exhibit Vainshtein screening of scalar fields. In this paper we apply the PPNV
formalism to the Quartic and Quintic Galileon theories for the first time. As
simple generalizations of standard scalar-tensor field theories they are
important guides for the generalization of parameterized approaches to the
effects of gravity beyond General Relativity. In the Quartic case, we find new
PPNV potentials for both screened and un-screened regions of spacetime, showing
that in principle these theories can be tested. In the Quintic case we show
that Vainshtein screening does not occur to Newtonian order, meaning that the
theory behaves as Brans-Dicke to this order, and we discuss possible higher
order effects.
