Ba5(BO3)3F single crystals of high optical quality and up to 1.5 cm in diameter were grown. Its transparency range is 0.23 to 6.6 μm (on 10% level). Direct allowed electronic transitions at the Γ-point give band gap values of 5.31 and 5.40 eV at 300 and 80 K, respectively. Luminescence is excited in the near-edge absorption bands near 265 and 365 nm. X-ray irradiation induces an additional absorption in dominant 252, 317 and 710 nm bands. Combined electron spin-resonance spectroscopy and theoretical analysis allow one to associate the three absorption peaks with O(5-), O(1-) and e6(-) (fluorine vacancy), respectively. The original transparency is restored after heating the crystal to 400 K and charge carrier release from traps with ET = 0.87 eV and s = 10(12) s(-1). Dispersion curves for the refractive indices were calculated and Sellmeier equations were built. Theoretical analysis shows strong localization of the Ba 5s and F 2s orbitals, strong ionicity of the Ba cations and strong covalency of the B-O bond. The optical properties of Ba5(BO3)3F are dominantly determined by electron transitions within the (BO3)(3-) groups, despite the transition between barium and oxygen also having a little contribution.