Several CuIn$_3$Te$_5$ single-crystal samples grown by the vertical Bridgman method have been studied. Changes in composition of the In/Cu atomic ratios in the 3.45–1.88 range have been detected along the ingots by X-ray energy-dispersive analysis. In the first-to-freeze region, Cu excess and In and Te depletions appear. From X-ray powder diffraction data we conclude that the crystals show the $P$-chalcopyrite-type structure, space group $P\bar{4}2c$, with lattice parameters $a$ = 6.1713 Å and $c$ = 12.329 Å, similar to that found in CuIn$_3$Se$_5$. The optical energy gaps, as determined by spectral ellipsometry, lie in the 1.83–1.93 eV range and change with composition. Micro-Raman spectra and infrared reflectance measurements confirm the presence of the crystallographic phase CuIn$_3$Te$_5$ and indicate a highly ordered Te sublattice and disordered Cu and In sublattices. Conduction types $n$ and $p$ are found, suggesting the possibility of intentional doping. The crystal density and gaps seem appropriate for their use in gamma-ray detectors.