The rare earth-free Mn5Ge3 compound shows magnetocaloric properties similar to those of pure Gd; therefore, it is a good candidate for magnetic refrigeration technology. In this work, we investigate the influence of chemical substitution on the crystal structure and the magnetic, thermodynamic, and magnetocaloric properties of a polycrystalline Mn5Ge3 compound prepared by induction melting. For this purpose, we replaced 5% of the Mn with Cr or Co and 5% of the Ge with B or Al. The additional chemical elements were shown not to change the crystal structure of the parent compound (space group P63/mcm, No. 193). In the case of the magnetic properties, all samples remained ferromagnetic with the ordering temperature (TC) lower than for the original compound (TC = 295(1) K). The exception was the sample with B, where we observed an increase in TC by 3 K. The maximum value of the magnetic entropy change, |∆Sm|MAX (for a magnetic field change of 5 T), decreased from 7.1(1) for Mn5Ge3 to 6.2(1), 6.8(1), 4.8(1), and 5.8(1) J kg−1 K−1 for the alloys with B, Al, Cr, and Co, respectively. The adiabatic temperature change (∆Tad) (for a magnetic field change of 1 T) was determined from the specific heat measurements and was equal to 1.1(1), 1.2(1), 1.2(1), 0.8(1), and 0.8(1) K for Mn5Ge3, Mn5Ge2.85B0.15, Mn5Ge2.85Al0.15, Mn4.75Cr0.25Ge3, and Mn4.75Co0.25Ge3, respectively. The obtained data were compared with those from the literature. It was found that the substitution allowed for tuning of the ordering temperature in a wide temperature range. At the same time, the reduction in the magnetocaloric parameters’ values was relatively small. Therefore, the produced Mn5Ge3-based alloys allow for the expansion of the operation temperature range of the parent compound as a magnetocaloric material.