We present a photometric and spectroscopic study of a reddened type Ic supernova (SN) 2005at. We report our results based on the available data of SN 2005at, including late-time observations from the Spitzer Space Telescope and the Hubble Space Telescope. In particular, late-time mid-infrared observations are something rare for type Ib/c SNe. In our study we find SN 2005at to be very similar photometrically and spectroscopically to another nearby type Ic SN 2007gr, underlining the prototypical nature of this well-followed type Ic event. The spectroscopy of both events shows similar narrow spectral line features. The radio observations of SN 2005at are consistent with fast evolution and low luminosity at radio wavelengths. The late-time Spitzer data suggest the presence of an unresolved light echo from interstellar dust and dust formation in the ejecta, both of which are unique observations for a type Ic SN. The late-time Hubble observations reveal a faint point source coincident with SN 2005at, which is very likely either a declining light echo of the SN or a compact cluster. For completeness we study ground-based pre-explosion archival images of the explosion site of SN 2005at, however this only yielded very shallow upper limits for the SN progenitor star. We derive a host galaxy extinction of $A_{V} ≈ 1.9$ mag for SN 2005at, which is relatively high for a SN in a normal spiral galaxy not viewed edge-on. ; Comment: 13 pages, 13 figures. Minor changes in text from v1. Published in A&A