This paper proposes a simple carrierbased PWM (CBPWM) technique to control the threeto five-phase Direct Matrix Converter (3×5 DMC). The proposed technique uses the indirect modulation approach to control the 3×5 DMC such as a threephase bidirectional rectifier followed by five-phase voltage source inverter (VSI). Based on this approach, it is possible to synthesize the desired five-phase output voltages with sinusoidal three-phase input currents and unity input power factor. A CBPWM method is suggested for each stage independently including both linear and overmodulation operating modes. By the proposed technique, in both operating modes, the maximum possible overall Voltage Transfer Ratio (VTR) is achieved. Moreover, this technique allows the input power factor to be controlled by controlling the input current displacement angle. The feasibility of the proposed technique has been verified by a series of simulation and experimental results based on Matlab/Simulink and dSPACE-DS1104 platform. The results show that a sinusoidal output and input waveforms can be achieved with a maximum possible VTR in the linear region. However, in the overmodulation region, a maximum possible VTR is achieved at the cost of some distortion of output and input waveforms. Therefore, this technique can be used for the application where a higher VTR is essential.