A prototype 5-GHz 500-kW CW klystron (model E3762 provided by Toshiba Electron Tubes & Devices Co. Ltd.) has been operating as the RF source for the lower hybrid current drive (LHCD) system in the KSTAR tokamak. In order to investigate how the efficiency of the 5-GHz 500-kW CW klystron prototype could be enhanced, the cavity design study is being carried out with simulation code based on the main klystron operation parameters. This is being done by simulating klystron performances for various cavity parameters including the number of cavities, inter-cavity distance, and cavity tuning frequencies. The simulation has been done with the FCI (field charge interaction) code aided by a matlab script for scanning input parameters. Initial set of scan parameters was obtained by benchmarking the E3762 klystron. It was possible to obtain optimized design parameters with better efficiency for a cavity system adopting a multi-cell output cavity. However, the multi-cell output cavity is prone to produce a self-oscillation due to the prolonged (several half RF periods) beam-field interaction along its multiple gaps. We have 2 checked the feasibility of the optimization by evaluating the stability of output cavity system. The stability is given by the ratio of a beam-loading conductance to the circuit conductance.