We report on new measurements of m-fold photodetachment (m=2-5) of carbon anions via K-shell excitation and ionization. The experiments were carried out employing the photon-ion merged-beams technique at a synchrotron light source. While previous measurements were restricted to double detachment (m=2) and to just the lowest-energy K-shell resonance at about 282 eV, our absolute experimental $m$-fold detachment cross sections at photon energies of up to 1000 eV exhibit a wealth of new thresholds and resonances. We tentatively identify these features with the aid of detailed atomic-structure calculations. In particular, we find unambiguous evidence for fivefold detachment via double K-hole production.