A joint theoretical and experimental study of the opto-electronic properties of Ta3N5 was conducted by means of ab initio calculations and ellipsometry measurements. Previous experimental work on Ta3N5 has not been conclusive regarding the direct or indirect nature of light absorption. Our work found excellent agreement between the optical spectrum computed using the BetheSalpeter Equation and the measured one, with two prominent features occurring at 2.1 and 2.5 eV assigned to direct transitions between N and Ta states. The computed optical gap, obtained from the G0W0 direct photoemission gap, including spin-orbit coupling, electron-phonon renormalization of the conduction band and exciton binding energy, was found to be in excellent agreement with measurements. Our results also showed that Ta3N5 is a highly anisotropic material with heavy holes in several directions, suggesting low hole mobilities, consistent with low measured photocurrents in the Ta3N5 literature.