A successful beam cleanup of a 5-mJ/200-1s pulsed solid-state laser system operating at 532-nm wavelength is demonstrated. In this beam cleanup system, a wave-front sensor-less adaptive optics (AO) system is set up with a 20-element bimorph mirror (BM), a high-voltage amplifier, a charge-coupled device camera, and a control software implementing the stochastic parallel gradient descent (SPGD) algorithm. The brightness of the laser focal spot is improved because the wave-front distortions have been compensated. The performance of this system is presented and the experimental results are analyzed.