  Over the past decade the discovery of three unique stellar populations and a
large number of confirmed pulsars within the globular cluster Terzan 5 has
raised questions over its classification. Using the long-term radio pulsar
timing of 36 millisecond pulsars in the cluster core, we provide new
measurements of key physical properties of the system. As Terzan 5 is located
within the galactic bulge, stellar crowding and reddening make optical and near
infrared observations difficult. Pulsar accelerations, however, allow us to
study the intrinsic characteristics of the cluster independent of reddening and
stellar crowding and probe the mass density profile without needing to quantify
the mass to light ratio. Relating the spin and orbital periods of each pulsar
to the acceleration predicted by a King model, we find a core density of
$1.58\times$10$^6$ M$_\odot$ pc$^{-3}$, a core radius of 0.16 pc, a pulsar
density profile $n\propto r^{-3.14}$, and a total mass of M$_{\rm
T}$($R_\perp<$1.0 pc)$\simeq3.0\times$10$^5$ M$_\odot$ assuming a cluster
distance of 5.9 kpc. Using this information we argue against Terzan 5 being a
disrupted dwarf galaxy and discuss the possibility of Terzan 5 being a fragment
of the Milky Way's proto-bulge. We also discuss whether low-mass pulsars were
formed via electron capture supernovae or exist in a core full of heavy white
dwarfs and hard binaries. Finally we provide an upper limit for the mass of a
possible black hole at the core of the cluster of 3.0$\times$10$^4$ M$_\odot$.
