  Mn_5Ge_3C_x films with x>0.5 were experimentally shown to exhibit a strongly
enhanced Curie temperature T_C compared to Mn_5Ge_3. In this letter we present
the results of our first principles calculations within Green's function
approach, focusing on the effect of carbon doping on the electronic and
magnetic properties of the Mn_5Ge_3. The calculated exchange coupling constants
revealed an enhancement of the ferromagnetic Mn-Mn interactions mediated by
carbon. The essentially increased T_C in Mn_5Ge_3C is well reproduced in our
Monte Carlo simulations and together with the decrease of the total
magnetisation is found to be predominantly of an electronic nature.
