The "Universitetskiy/Tatyana" supersmall satellite was launched on January 20, 2005. Despite the fact that 2005 was the quiet Sun year, several solar energetic particle events were observed. Energy spectra of proton fluxes for five solar events were studied using data from the "Universitetskiy/Tatyana" supersmall satellite flying on the polar orbit at the ~950 km altitudes and with the 83 inclination. Proton fluxes were measured over a wide range of the energy (E>1 MeV) by the instrument designed and created at SINP MSU. The solar energetic particle distribution (peaked values of fluxes during a solar event) was described by a power law function of rigidity. Spectral indexes of energy spectra for proton fluxes measured on board "Universitetskiy/Tatyana" and GOES satellites fit satisfactory. Features of solar energetic particle event occurrence in quiet Sun years are discussed. Identity of studied energy spectra with ones measured during other periods of solar activity is shown.