The photodissociation of mass-selected linear carbon clusters (C-n, n = 4-6) is studied using fast beam photofragment translational spectroscopy. The photofragment yield (PFY) spectra consist of several continua spanning the whole visible and ultraviolet region. The product mass distributions for dissociation of C-n clusters are dominated by C-3 and its partner fragment Cn-3, although some minor channels are also identified for dissociation of C-4 and C-5 clusters. Translational energy P(E-T) distributions for the C-3 + Cn-3 channel were measured at several photolysis energies. The PFY spectra and P(E-T) distributions indicate that multiphoton dissociation occurs at photon energies below the dissociation threshold and that both single-photon and multiphoton dissociation occur above the threshold. The one-photon components of the P(E-T) distributions can be modeled by phase space theory (PST), suggesting that photoexcitation is followed by internal conversion to the ground state. The PST analysis yields dissociation energies for C-n,--> C-3 + Cn-3 in reasonable agreement with recent Knudsen effusion mass spectrometry measurements.