The Ξ_{c}^{+}K^{-} mass spectrum is studied with a sample of pp collision data corresponding to an integrated luminosity of 3.3 fb^{-1}, collected by the LHCb experiment. The Ξ_{c}^{+} is reconstructed in the decay mode pK^{-}π^{+}. Five new, narrow excited Ω_{c}^{0} states are observed: the Ω_{c}(3000)^{0}, Ω_{c}(3050)^{0}, Ω_{c}(3066)^{0}, Ω_{c}(3090)^{0}, and Ω_{c}(3119)^{0}. Measurements of their masses and widths are reported.