This paper presents a model of a quintuple-layer composite beam composed of functionally graded materials (FGMs) and shear connectors. A finite element model is developed based on the first-order shear deformation theory (FSDT) of Timoshenko, using a two-node beam element with eleven degrees of freedom per node. The interlayer sliding interaction is taken into account in the formulation. Based on the proposed theory, a computational program is implemented in the MATLAB environment and validated against various benchmark models. The results obtained from this study provide a foundation for further developments, including free vibration analysis and dynamic response investigations of complex beam structures.