Nowadays, companies are in the process of renewing their manufacturing lines by equipping them with modern five-axis CNC (computer numerical control) machining centers. The decision to select between different five-axis CNC machining centers, with similar technological capabilities is a difficult process, so the main goal of this work was to develop a method for assisting it. The proposed approach relies on seven technical criteria, four quantitative ones (traverse speed, thrust, spindle power, and spindle speed) which can be expressed by crisp numerical values, while the other three (flexibility, operation easiness, and setup time) are qualitative ones. The analytic hierarchy process (AHP) was used for ordering four variants of five-axis CNC milling machining centers. The qualitative criteria were processed using fuzzy systems to be expressed by crisp numerical values, suitable for AHP. Finally, the four variants of five-axis CNC milling machining centers were hierarchized and the best one was chosen. A sensitivity analysis was also unfolded to certify the robustness of the AHP.