<p>The tolerances of key moving components are critical factors influencing the final machining error in the design, manufacturing, and assembly of machine tools. However, the precise mechanism linking tolerances to machining errors remains insufficiently understood. This leads to a heavy dependence on the experience of engineers for tolerance design. However, human expertise may be influenced by subjective factors. Such subjectivity introduces variability that may increase manufacturing costs. To handle this complication, this paper proposes a method for predicting machining errors in five-axis machine tools considering the tolerances of key moving components. Firstly, the structure and kinematic characteristics of five-axis machine tools are analyzed, and the mapping relationship between axis motion tolerances and geometric errors is represented using the Fourier series. Then, a volumetric error prediction model for the five-axis machine tool is developed based on multi-body system theory and homogeneous transformation matrices, followed by deriving a machining error model according to the machining method of the workpiece. Finally, machining experiments are carried out on the five-axis machine tool and measured with a Coordinate Measuring Machine. The results show that the maximum deviation between predicted and measured values is less than 10.00%. These findings provide theoretical support for the tolerance design of five-axis machine tools, helping to reduce manufacturing costs and improve machining accuracy.</p>