  We report on ground-based and HST(+STIS) imaging of the afterglow and host
galaxy of the Gamma-Ray Burst (GRB) of March 5 2002. The GRB occurred in a
R=25.17+/-0.14 galaxy, which apparently is part of an interacting system. The
lightcurve of the optical afterglow shows a rebrightening, or at least a
plateau, 12--16 days after the gamma-ray event. UBVRIK' multi-band imaging of
the afterglow ~12 days after the GRB reveals a blue spectral energy
distribution (SED). The SED is consistent with a power-law with a spectral
index of \beta=-0.63+/-0.16, but there is tentative evidence for deviations
away from a power-law. Unfortunately, a spectroscopic redshift has not been
secured for GRB020305. From the SED we impose a redshift upper limit of z ~<
2.8, hence excluding the pseudo redshift of 4.6 reported for this burst. We
discuss the possibilities for explaining the lightcurve, SED and host galaxy
properties for GRB 020305. The most natural interpretation of the lightcurve
and the SED is an associated supernova (SN). Our data can not precisely
determine the redshift of the GRB. The most favoured explanation is a low
redshift (z~0.2) SN, but a higher redshift (z>0.5) SN can not be excluded. We
also discuss less likely scenarios not based on SNe, like a burst occurring in
a z=2.5 galaxy with an extinction curve similar to that of the Milky Way.
