  We measure how the slope $\alpha$ of the stellar mass function (MF) changes
as a function of clustercentric distance $r$ in five Galactic globular clusters
and compare $\alpha(r)$ to predictions from direct $N$-body star cluster
simulations. Theoretical studies predict that $\alpha(r)$ (which traces the
degree of mass segregation in a cluster) should steepen with time as a cluster
undergoes two-body relaxation and that the amount by which the global MF can
evolve from its initial state due to stellar escape is directly linked to
$\alpha(r)$. We find that the amount of mass segregation in M10, NGC 6218, and
NGC 6981 is consistent with their dynamical ages, but only the global MF of M10
is consistent with its degree of mass segregation as well. NGC 5466 and NGC
6101 on the other hand appear to be less segregated than their dynamical ages
would indicate. Furthermore, despite the fact that the escape rate of stars in
non-segregated clusters is independent of stellar mass, both NGC 5466 and NGC
6101 have near-flat MFs. We discuss various mechanisms which could produce
non-segregated clusters with near-flat MFs, including higher mass-loss rates
and black hole retention, but argue that for some clusters (NGC 5466 and NGC
6101) explaining the present-day properties might require either a
non-universal IMF or a much more complex dynamical history.
