The atomic structure and surface energies of several low-index surfaces (0001), (11¯00) and (112¯0) of Ti5Si3 in dependence on their termination were calculated by the projector augmented-wave method within the density functional theory. It was revealed that the mixed TiSi-terminated (0001) surface is stable within the wide range of change in the Ti chemical potential. However, the Ti-terminated Ti5Si3(0001) surface is slightly lower in energy in the Ti-rich limit. The oxygen adsorption on the stable Ti5Si3(0001) surface with TiSi termination was also studied. It was shown that the three-fold coordinated F1 position in the center of the triangle formed by surface titanium atoms is the most preferred for oxygen adsorption on the surface. The appearance of silicon as neighbors of oxygen in other considered F-positions leads to a decrease in the adsorption energy. The factors responsible for the increase/decrease in the oxygen adsorption energy in the considered positions on the titanium silicide surface are discussed.