A mathematical modeling of the time evolution of the populations of the states of a five-level molecule during transformation of resonant monochromatic irradiation and spontaneous emission from the highest-energy state excited by a short pulse of light is performed. The formalism of the optical Bloch equations and quantum theory of radiation are applied a composite system consisting of a molecule and a quantized radiation field. The results of simulation of the evolution of the population of the states of the molecule in the case of spontaneous emission are similar for both of these two approaches, but differ significantly in the case of conversion by the molecule of monochromatic radiation. These differences are the greater, the higher the intensity of resonance Rayleigh scattering or (and) relaxed fluorescence, as a result of which the molecule returns to the initial ground state. An explanation of the nature of these differences is given. Keywords: mathematical modeling, photophysical and photochemical transformations of molecules, optical Bloch equations, quantum theory of radiation DOI: 10.1134/S1990793117020099