  The HST's WFPC2 has several advantages over ground--based observations for
the study of globular cluster luminosity functions (GCLFs) and distance
determination. Here we present WFPC2 data on the globular clusters associated
with NGC 5846. This giant elliptical is the dominant galaxy in a small, compact
group located ~ 13 Mpc beyond the Virgo cluster. We have detected over 1200
globular clusters in three (central, north and south) separate pointings. The
luminosity function in each of these pointings are statistically the same,
indicating that the mean luminosity (mass) does not vary between ~ 3 and 30 kpc
from the galaxy center. This suggests that dynamical friction and bulge
shocking destruction processes are insignificant. We have fit a Gaussian and
t_5 profile to the GCLF (of the combined pointings) and find that it is well
represented by a turnover magnitude of m^0_V = 25.05 +/- 0.10 and a dispersion
of sigma = 1.34 +/- 0.06. Our 50% completeness level is ~ 1 mag fainter than
the turnover. After applying a metallicity correction to the `universal' GCLF
turnover magnitude, we derive a distance modulus of (m--M) = 32.32 +/- 0.23.
For a group velocity V_{CMB} = 1883 +/- 28 km/s, the Hubble constant is H_o =
65 +/- 8 km/s/Mpc.
