Single crystals of monoclinic La5Co2Ge3 were grown using a self-flux method and were characterized by room-temperature powder x-ray diffraction, anisotropic temperature- and field-dependent magnetization, temperature-dependent resistivity, specific heat, and muon spin rotation. La5Co2Ge3 has a Curie temperature (T-C) of 3.8 K and clear signatures of ferromagnetism in magnetization and mu SR data, as well as a clear loss of spin disorder scattering in resistivity data and a sharp specific heat anomaly. The magnetism associated with La5Co2Ge3 is itinerant has a change in the entropy at T-C of similar or equal to 0.05R ln 2 per mol Co and has a low-field saturated moment of similar to 0.1 mu(B)/Co, making it a rare, itinerant, small moment, low-T-C compound.