The formation enthalpy, electronic structures, and elastic moduli of the intermetallic compound Ti5Si3 with substitutions Zr, V, Nb, and Cr are investigated by using first-principles methods based on the density-functional theory. Our calculation shows that the site occupancy behaviors of alloying elements in Ti5Si3, determined by their atom radius, are consistent with the available experimental observations. Furthermore, using the Voigt–Reuss–Hill (VRH) approximation method, we obtained the bulk modulus B, shear modulus G, and the Young’s modulus E. Among these four substitutions, the V, Nb, and Cr substitutions can improve the ductility of Ti5Si3 effectively, while Zr substitution has little effect on the elastic properties of Ti5Si3. The elastic property variations of Ti5Si3 due to different substitutions are found to be correlated with the Me4d–Me4d antibonding and the strengthened Me4d–Si bonding in the solids.