To understand the structural stability, physical properties, and hardness of the Rh–Si system, we have performed systematic first-principles crystal structure searches for various stoichiometries of rhodium silicides, utilizing the particle swarm optimization method. A new stable stoichiometry, Rh4Si5 with space group P21/m, has been found at atmospheric pressure, complementing the three well-known rhodium silicides of Rh2Si (Pnma), Rh5Si3 (Pbam), and RhSi (Pnma). Our calculations of the structural and mechanical properties of the known phases are in excellent agreement with the available experimental data and similar theoretical calculations. The elastic, electronic, and hardness properties of the Rh–Si stoichiometries are discussed. Our results suggest that the new rhodium silicide Rh4Si5 (P21/m) is a potentially hard material with the hardness of 20.1 GPa.