A five mirror system with a reduction magnification(M=+1/5) is designed for DUV optical lithography. Initially, numerical solutions of all zero 3rd order aberrations and zero 5th order spherical aberration are obtained for the spherical mirror system. Next, by the optimization method, the aspherization is carried out to the two spherical mirrors to obtain a system that has as less residual aberrations, higher NA and improved MTF as possible. We have finally obtained the system of which NA is 0.45 and the resolution is about 500 cycles/mm at the 50% MTF value criterion and the depth of focus of $1.0{mu}m$ for the nearly incoherent illumination$({sigma}=1.0)$ and the wavelength of 0.248 m(KrF excimer laser line).