Relaxation of stored charge carriers in the persistent-photoconductivity (PPC) mode in a CdS0.5Se0.5 semiconductor alloy has been investigated. The relaxation time constant of PPC is systematically measured as a function of temperature, from which the recombination barrier height Erec has been determined. Low-temperature exciton luminescence has also been investigated and the exciton transition linewidth, which is broadened due to the presence of compositional fluctuations, is measured. The values of Erec deduced from the measured exciton linewidth and the localized-to-delocalized transition temperature in the PPC mode are consistent with the results obtained from the PPC-decay measurements. These experimental results are consistent with our previous interpretation that PPC in CdS0.5Se0.5 semiconductor alloys is caused by random local potential fluctuations induced by compositional fluctuations.