We have examined the superconducting ground state properties of the caged type compound Sc$_5$Rh$_6$Sn$_{18}$ using magnetization, heat capacity, and muon-spin relaxation or rotation ($mu$SR) measurements. Magnetization measurements indicate type-II superconductivity with an upper critical field $mu_0H_{c2}(0)$ = 7.24 T. The zero-field cooled and field cooled susceptibility measurements unveil an onset of diamagnetic signal below $T_{bf c}$ = 4.4 K. The interpretation of the heat capacity results below $T_{bf c}$ using the $alpha-$BCS model unveils the value of $alpha$ = 2.65, which gives the dimensionless ratio 2$Delta(0)/k_B T_{bf c}$ = 5.3, intimating that Sc$_5$Rh$_6$Sn$_{18}$ is a strong-coupling BCS superconductor. The zero-field $mu$SR measurements in the longitudinal geometry exhibit a signature of a spontaneous appearance of the internal magnetic field below the superconducting transition temperature, indicating that the superconducting state is characterized by the broken time-reversal symmetry (TRS). We have compared the results of broken TRS in Sc$_5$Rh$_6$Sn$_{18}$ with that observed in R$_5$Rh$_6$Sn$_{18}$ (R = Lu and Y).
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