Large-scale ab initio coupled cluster and multi-reference configuration interaction calculations (MRD-CI) are carried out to determine the equilibrium geometry and the vertical electronic spectrum of linear C-5(+). Contrary to prior theoretical estimates we find three low-lying states within an energy range of 0.3 eV: (2)Sigma (+)(u), (2)Sigma (+)(g) and (2)Pi (g) and a symmetric arrangement of nuclei. Transitions from (2)Sigma (+)(u) to these low-lying states are dipole-allowed; sizeable oscillator strengths are computed for the 2 Pi (+)(g) <--X(2)Sigma (+)(u): transition at 2.62 eV and the (g)Sigma (g) <--X(2)Sigma (+)(u) transition at 3.36 eV and should give a guide to spectroscopic identification of linear C-5(+).