The results of Culler and Shalen for 2,3 or 4-free hyperbolic 3-manifolds are
contingent on properties specific to and special about rank two subgroups of a
free group. Here we determine what construction and algebraic information is
required in order to make a geometric statement about $M$, a closed, orientable
hyperbolic manifold with $k$-free fundamental group, for any value of $k$
greater than four. Main results are both to show what the formulation of the
general statement should be, for which Culler and Shalen's result is a special
case, and that it is true modulo a group-theoretic conjecture. A major result
is in the $k=5$ case of the geometric statement. Specifically, I show that the
required group-theoretic conjecture is in fact true in this case, and so the
proposed geometric statement when $M$ is 5-free is indeed a theorem. One can
then use the existence of a point and knowledge about $\pi_1(M,P)$ resulting
from this theorem to attempt to improve the known lower bound on the volume of
$M$, which is currently 3.44