The oxygen absorption energy and its migration barriers in titanium silicide with composition Ti5Si3 and hexagonal structure have been calculated by using the projector augmented-wave method within the electron density functional theory. We have derived analytical expressions for the temperature-dependent diffusion coefficients along two crystallographic directions using Landman's method and calculated the activation energies and the pre-exponential factor. The mechanism of oxygen diffusion in the bulk Ti5Si3 is discussed. It is shown that the obtained diffusion coefficient of oxygen in this silicide is comparable with experimental ones for metal oxides such as Al2O3, SiO2, Cr2O3.