Thin disk laser experiments with Yb:LuAG (Yb:Lu(3)Al(5)O(12)) were performed leading to 5 kW of output power and an optical-to-optical efficiency exceeding 60%. Comparative analyses of the laser relevant parameters of Yb:LuAG and Yb:YAG were carried out. While the spectroscopic properties were found to be nearly identical, investigations of the thermal conductivities revealed a 20% higher value for Yb:LuAG at Yb(3+)-doping concentrations of about 10%. Due to the superior thermal conductivity with respect to Yb:YAG, Yb:LuAG offers thus the potential of improved performance in high power thin disk laser applications.