The atomic and electronic structures, the elastic moduli, the vibrational frequencies, and the thermodynamic characteristics of the Ti5Si3 titanium silicide are calculated by the projector augmented wave method within the density functional theory. The Fermi surface is calculated and the electron velocity on all its four sheets is estimated. An analysis of the spatial dependence of linear compressibility, Young’s modulus, and shear modulus demonstrates their weak anisotropy, and the anisotropy of Poisson’s ratio is more pronounced. The phonon spectrum of the titanium silicide is calculated and its thermodynamic characteristics are estimated. On the whole, the calculation results are in good agreement with the experimental results.