Multilevel inverters are popular for renewable energy applications. This paper presents a technique for harmonic elimination in a five level cascaded H-Bridge multilevel inverter. The technique is based on computation of switching angles using Chebyshev polynomials. The method involves simple mathematical calculations to arrive at the desired switching angles for harmonic elimination. In this paper, Chebyshev polynomials are utilized to calculate the switching angles for eliminating the 3rd and 5th harmonic in a five level multilevel inverter system for a modulation index of 0.8. The work evaluates the reduction in the total harmonic distortion of the five level inverter system by eliminating specific harmonic from the multilevel inverter system. Further, a comparison is established to evaluate the power quality of a selective harmonic eliminated system with a conventional five level multi carrier based pulse width modulated inverter. MATLAB-SIMULINK environment is used to verify the simulation results. © 2016 IEEE.