Here we investigate single crystals of CaCo$_{5}$As$_{3}$ by means of single crystal X-ray diffraction, microprobe, magnetic susceptibility, heat capacity, and pressure-dependent transport measurements. CaCo$_{5}$As$_{3}$ shares the same structure of CaFe$_{4}$As$_{3}$ with an additional Co atom filling a lattice vacancy and undergoes a magnetic transition at $T_{M} = 16$ K associated with a frustrated magnetic order. CaCo$_{5}$As$_{3}$ displays metallic behavior and its Sommerfeld coefficient ($gamma = 70$ mJ/mol.K$^{2}$) indicates a moderate enhancement of electron-electron correlations. Transport data under pressures to $2.5$ GPa reveal a suppression of $T_{M}$ at a rate of $-0.008$ K/GPa. First-principle electronic structure calculations show a complex 3D band structure and magnetic moments that depend on the local environment at each Co site. Our results are compared with previous data on CaFe$_{4}$As$_{3}$ and provide a scenario for a magnetically frustrated ground state in this family of compounds.