The recent identification of HRgC5N (Rg = Kr, Xe) in a cryogenic matrix calls for an in-depth theoretical study on these compounds. Here we present the results of CCSD(T), MP2, and DFT calculations concerning the molecular structure, stability, and vibrational spectroscopy. The procedure combining CCSD(T) calculations for variable H-Rg distances with the anharmonic description of the corresponding stretching vibration, based on a Morse-type potential energy function, was proposed and has led to good agreement between computational and experimental values for H-Rg stretching frequencies, at relatively low computational costs. High Raman scattering activity of HRgC5N and of its isomers, predicted at the DFT level, gives some prospects for the detection of these molecules with a method alternative to the IR absorption spectroscopy.