  For $d=4, 5, 6$, we exhibit the first examples of complete finite volume
hyperbolic $d$-manifolds $M$ with cusps such that infinitely many $d$-orbifolds
$M_{m}$ obtained from $M$ by generalized Dehn filling admit properly convex
real projective structures. The orbifold fundamental groups of $M_m$ are
Gromov-hyperbolic relative to a collection of subgroups virtually isomorphic to
$\mathbb{Z}^{d-2}$, hence the images of the developing maps of the projective
structures on $M_m$ are new examples of divisible properly convex domains of
the projective $d$-space which are not strictly convex, in contrast to the
previous examples of Benoist.
