  We study the mass and anisotropy distribution of the giant elliptical galaxy
NGC 5846 using stars, as well as the red and blue globular cluster (GC)
subpopulations. We break degeneracies in the dynamical models by taking
advantage of the different phase space distributions of the two GC
subpopulations to unambiguously constrain the mass of the galaxy and the
anisotropy of the GC system. Red GCs show the same spatial distribution and
behaviour as the starlight, whereas blue GCs have a shallower density profile,
a larger velocity dispersion and a lower kurtosis, all of which suggest a
different orbital distribution. We use a dispersion-kurtosis Jeans analysis and
find that the solutions of separate analyses for the two GC subpopulations
overlap in the halo parameter space. The solution converges on a massive dark
matter halo, consistent with expectations from $\Lambda$CDM and WMAP7 cosmology
in terms of virial mass ($\log M_{DM} \sim13.3 M_{sun}$) and concentration
($c_{vir}\sim8$). This is the first such analysis that solves the dynamics of
the different GC subpopulations in a self-consistent manner. Our method
improves the uncertainties on the halo parameter determination by a factor of
two and opens new avenues for the use of elliptical galaxy dynamics as tests of
predictions from cosmological simulations. The implied stellar mass-to-light
ratio derived from the dynamical modelling is fully consistent with a Salpeter
initial mass function (IMF) and rules out a bottom light IMF. The different GC
subpopulations show markedly distinct orbital distributions at large radii,
with red GCs having an anisotropy parameter $\beta\sim0.4$ outside $\sim3R_e$,
and the blue GCs having $\beta\sim0.15$ at the same radii, while centrally
($\sim1R_e$) they are both isotropic. We discuss the implications of our
findings within the two-phase formation scenario for early-type galaxies.
