Under the framework of density functional theory, we systematically explore the geometric, electronic, transport, and thermal properties of a novel 2D pentagonal monolayer of GeC5. Our calculations show that the structure is dynamically and mechanically stable. Simulated results indicate that the predicted monolayer is an indirect semiconductor with a band gap of 1.77 eV. Using the Bardeen and Shockley formula, the carrier mobility of the electrons is found to be 824.41 cm2 V−1 S−1, while that of holes registers a more significant value of 4433.84 cm2 V−1 S−1. The lattice thermal conductivity for the undoped system was calculated using the Slack model, recording values of 13.46 W/(m.K), 6.73 W/(m.K), and 4.49 W/(m.K) at 300K, 600K, and 900K, respectively. In the case of electron doping, the figure of merit (ZT) is only significant along the x-direction. ZT reaches a maximum value of 2.97 at T = 300K for an energy of 0.79 eV above the Fermi level. Hole doping, however, does not lead to exciting results due to the shallow ZT values. All reported results are vacuum-free, enabling an accurate and direct comparison with experimental data whenever available. The obtained electronic properties suggest that the penta-GeC5 monolayer is a promising candidate for new electronic device applications. Additionally, when appropriately doped, the figure of merit of penta-GeC5 is expected to increase with temperature, thus making it a key ingredient in producing thermoelectric devices on the nanoscale.