The first step in the Fischer-Tropsch reaction is the production of C1 monomers by the dissociation of the C-O bond. Although Fe is the active metal, it is well known that under typical reaction conditions, it changes into various carbide phases. The Hägg carbide (χ-Fe5C2) phase is usually considered as the catalytically active phase. We carried out a comprehensive DFT study of CO dissociation on various surface terminations of the Hägg carbide, selected on their specific site topology and the presence of stepped sites. Based on the reaction energetics, we identified several feasible CO dissociation pathways over the Hägg carbide. In this study, we have compared the direct CO dissociation with H- and C-assisted CO dissociation mechanisms. We demonstrated that the reaction rate for CO dissociation critically depends on the presence and topology of interstitial C atoms close to the active site. Typically, the CO dissociation proceeds via a direct C-O bond scission mechanism on the stepped sites on the Fe carbide surface. We have shown a preference for the direct CO dissociation on the surfaces with a stepped character. The H-assisted CO dissociation, via a CHO intermediate, was preferred when the surface did not have a clear stepped character. We have also shown that activation barriers for dissociation are highly dependent on the surface termination. With a consistent data set and including migration corrections, we then compared the CO dissociation rates based on a simplified kinetic model. With this model, we showed that besides the activation energy, the adsorption energy of the CO, the C and the O species are important for the reaction rate as well. We found that the most active surface termination is a (111) surface cut in such a way that the surface exposes B5 sites that are not occupied by the C atoms. On these B5 sites, the direct CO dissociation presents the highest rate.