  We determine the gravitational interaction between two compact bodies up to
the sixth power in Newton's constant GN, in the static limit. This result is
achieved within the effective field theory approach to General Relativity, and
exploits a manifest factorization property of static diagrams which allows to
derive static post Newtonian (PN) contributions of (2n+1)-order in terms of
lower order ones. We recompute in this fashion the 1PN and 3PN static
potential, and present the novel 5PN contribution.
