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 β= -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 GRB 020305. 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. © ESO 2005.