We report the transport, thermodynamic, and magnetic properties of stoichiometric single-crystalline ${\mathrm{Ce}}_{5}{\mathrm{CoGe}}_{2}$ by measuring the electrical resistivity, specific heat, DC magnetization, and AC susceptibility. ${\mathrm{Ce}}_{5}{\mathrm{CoGe}}_{2}$ crystallizes in an orthorhombic structure with space group $Pnma$, and undergoes a long-range ferromagnetic (FM) transition at ${T}_{\mathrm{C}}=10.9$ K, showing a strong magnetic anisotropy at low temperature with an easy $a$ axis. Furthermore, the AC susceptibility exhibits a single cusp with a clear frequency dependence. Detailed analysis suggests that a cluster-type spin glass (SG) state appears below the freezing temperature ${T}_{\mathrm{f}}=10.9(1)$ K in ${\mathrm{Ce}}_{5}{\mathrm{CoGe}}_{2}$, which is identical to ${T}_{\mathrm{C}}$ within error bar. These findings suggest the coexistence of FM order and frustrated glassy magnetic components below ${T}_{\mathrm{C}}$ in ${\mathrm{Ce}}_{5}{\mathrm{CoGe}}_{2}$.