  We present a new method to combine multimass equilibrium dynamical models and
pulsar timing data to constrain the mass distribution and remnant populations
of Milky Way globular clusters (GCs). We first apply this method to 47 Tuc, a
cluster for which there exists an abundance of stellar kinematic data and which
is also host to a large population of millisecond pulsars. We demonstrate that
the pulsar timing data allow us to place strong constraints on the overall mass
distribution and remnant populations even without fitting on stellar
kinematics. Our models favor a small population of stellar-mass BHs in this
cluster (with a total mass of $412^{+77}_{-146} \mathrm{M_\odot}$), arguing
against the need for a large ($ > 2000 \ \mathrm{M_\odot}$) central
intermediate-mass black hole. We then apply the method to Terzan 5, a heavily
obscured bulge cluster which hosts the largest population of millisecond
pulsars of any Milky Way GC and for which the collection of conventional
stellar kinematic data is very limited. We improve existing constraints on the
mass distribution and structural parameters of this cluster and place stringent
constraints on its black hole content, finding an upper limit on the mass in
BHs of $\sim 4500 \ \mathrm{M_\odot}$. This method allows us to probe the
central dynamics of GCs even in the absence of stellar kinematic data and can
be easily applied to other GCs with pulsar timing data, for which datasets will
continue to grow with the next generation of radio telescopes.
