  We construct a suite of discrete chemo-dynamical models of the giant
elliptical galaxy NGC 5846. These models are a powerful tool to constrain both
the mass distribution and internal dynamics of multiple tracer populations. We
use Jeans models to simultaneously fit stellar kinematics within the effective
radius $R_{\rm e}$, planetary nebula (PN) radial velocities out to $3\, R_{\rm
e}$, and globular cluster (GC) radial velocities and colours out to $6\,R_{\rm
e}$. The best-fitting model is a cored DM halo which contributes $\sim 10\%$ of
the total mass within $1\,R_{\rm e}$, and $67\% \pm 10\%$ within $6\,R_{\rm
e}$, although a cusped DM halo is also acceptable. The red GCs exhibit mild
rotation with $v_{\rm max}/\sigma_0 \sim 0.3$ in the region $R > \,R_{\rm e}$,
aligned with but counter-rotating to the stars in the inner parts, while the
blue GCs and PNe kinematics are consistent with no rotation. The red GCs are
tangentially anisotropic, the blue GCs are mildly radially anisotropic, and the
PNe vary from radially to tangentially anisotropic from the inner to the outer
region. This is confirmed by general made-to-measure models. The tangential
anisotropy of the red GCs in the inner regions could stem from the preferential
destruction of red GCs on more radial orbits, while their outer tangential
anisotropy -- similar to the PNe in this region -- has no good explanation. The
mild radial anisotropy of the blue GCs is consistent with an accretion
scenario.
