This paper presented an analytical and closed-form solution for the harmonic contents that were injected in the five-level inverters from asymmetrical DC sources or batteries which were suitable for renewable energy sources. In the five-level inverters, two DC sources V1 and V2 were used to synthesize the output voltage. Therefore, two transcendental equations were formulated for the fundamental and the third harmonic orders based on the unequal DC sources V1 and V2. These transcendental equations were solved analytically for low switching control technique. The proposed solution included the modulation index change which resulted in changing the fundamental component. Therefore, two switching angles are formulated and solved analytically to control the amplitude of the fundamental voltage and cancel the third order harmonic. A well-known third order equation was generated. Thus, a closed-form solution for the above two switching angles will be generated in terms of the modulation index. The proposed solution was tested for a wide range of V1/V2 ratio. Some selected simulation and experimental results were provided to validate the proposed method for wide ranges of both modulation index and V1/V2 ratio.