Most of the modern catalysts are based on precious metals and rear-earth elements making some reactions of organic synthesis economically insolvent. Density functional theory calculations here are used to describe several differently oriented surfaces of higher tungsten boride WB5-x, along with their catalytic activity for CO oxidation reaction. Based on our findings, WB5-x appears as efficient alternative catalyst for CO oxidation. Computed surface energies enable the use of Wulff construction to determine the equilibrium shape of WB5-x particles. It is found that (010) and (101) facets terminated by boron and tungsten, respectively, are the mainly exposed surfaces for which the various gas agents (СО, СO2, H2, N2, O2, NO, NO2, H2O, NH3, SO2) adsorption is evaluated, to reveal promising prospects of applications. CO oxidation on B-rich (010) and W-rich (101) surfaces is further explored in more detail by analyzing the charge redistribution during the adsorption of CO and O2 molecules. It is found that CO oxidation displays relatively low energy barriers. Implications of the present results, the WB5-x effects on the CO oxidation, and potential use in automotive, chemical, mining industries are discussed.