Density functional theory and Boltzmann transport equations are employed to calculate the thermoelectric transport coefficients, electronic structure and optical properties of bulk garnet-like oxides Li5La3M2O12 (M = Nb, Ta) single crystals. The calculated energy band structure and density of states disclose the metallic nature for both compounds. Li5La3Nb2O12 possesses a greater density of states around Fermi level than Li5La3Ta2O12, which is due to the Nb/Ta-d states. The calculated electronic charge density of both compounds indicates a dominant ionic character of chemical bonding. Optical susceptibilities, including the real and imaginary parts of the optical dielectric functions, reflectivity and energy loss function, are calculated. The reflectivity of the investigated compounds reaches to 60% in the UV region. The maximum peaks in the energy loss function are due to the plasmon resonance with the decreasing energy of electrons instead of surface plasmon loss. The Seebeck coefficients, power factor, figure of merit, heat capacity as well as electrical and thermal conductivities are calculated as a function of temperature for relaxed structures, using BotlzTraP code at constant pressure, which is strongly affected by carrier and intrinsic defects concentration. Our calculated result shows that Li5La3Ta2O12 is better thermoelectric material than Li5La3Nb2O12 along the entire temperature ranges.