Conventional superconductors are robust diamagnets that expel magnetic fields through the Meissner effect. It would therefore be unexpected if a superconducting ground state would support spontaneous magnetics fields. Such broken time-reversal symmetry states have been suggested for the high-temperature superconductors, but their identification remains experimentally controversial. We present magnetization, heat capacity, zero field and transverse field muon spin relaxation experiments on the recently discovered caged type superconductor Y5Rh6Sn18 ( TC= 3.0 K). The electronic heat capacity of Y5Rh6Sn18 shows a T(3) dependence below Tc indicating an anisotropic superconducting gap with a point node. This result is in sharp contrast to that observed in the isostructural Lu5Rh6Sn18 which is a strong coupling s-wave superconductor. The temperature dependence of the deduced superfluid in density Y5Rh6Sn18 is consistent with a BCS s-wave gap function, while the zero-field muon spin relaxation measurements strongly evidences unconventional superconductivity through a spontaneous appearance of an internal magnetic field below the superconducting transition temperature, signifying that the superconducting state is categorized by the broken time-reversal symmetry.