The increased accessibility of the tool achieved by using 5-axis roughing reduces the overall machining time of complex parts by reducing or eliminating the re-roughing and semi-finishing operations thereby decreasing the volume of remaining material before finishing operations. However, 5-axis milling generates significant variations in tool orientation which, combined with the high tool engagement in the material required by the roughing conditions, can be penalizing. Controlling these variations is therefore mandatory to guarantee the tool life, the productivity and the quality of the roughing operation. Thus, a multi-objective optimization is proposed to define the successive orientations of the tool axis along the path that minimize the feedrate slowdowns and thus the machining time, balance the pushing or pulling machining configurations and respect the programmed scallops heights of the machined surface. In this work, the tool path is defined by two curves, one constraining the position of the tool and the other its orientation allowing for a parametric synchronization to conduct the optimization. From the definition of the weights of each of the minimization objective functions, it is possible to find a tool axis orientation solution that satisfies the given constraints all along the path. The application on a test part by simulation and machining highlights the effectiveness of the proposed approach and the advantages of controlling the evolution of the tool axis orientation in 5-axis roughing.