Density functional theory calculations have been carried out on the CO/H-2 coadsorption on the (001), (110), and (100) surfaces of Fe5C2 for the understanding of the Fischer-Tropsch synthesis (FTS) mechanism. The stable surface species changes with the variation of the H-2 and CO coverage. Along with dissociated hydrogen and adsorbed CO in 2-, 3-, and 4-fold configurations, methylidyne (C,H) (C-s, surface carbon), ketenylidene (CsCO), ketenyl (CsHCO), ketene (CsH2CO), and carbon suboxide (CsC2O2) are computed as thermodynamically stable surface species on Fe5C2(001) and Fe5C2(110) containing both surface iron and carbon atoms. These surface carbon species can be considered as the preliminary stages for FTS. On Fe5C2(100) with only iron atoms on the surface layer, the stable surface species is dissociated hydrogen and CO with top and 2-fold configurations. The bonding nature of these adsorbed carbon species has been analyzed.