Phase behavior and dynamics in blends of a liquid crystal 4-cyano-4'-n-pentylbiphenyl (5CB) and polystyrene(PS) were investigated by using dielectric spectroscopy. The blends exhibit phase separation of a UCST type. Below the phase-separation temperature, the blends separate into the isotropic PS-rich and 5CB-rich phases. With decreasing temperature the 5CB-rich phase transforms into the nematic liquid crystalline state and subsequently into the regular crystalline states. The nematic phase supercools about 30 K below the nematic-to-crystal transition point T-NC. Optical micrographs of blends indicate that spherical 5CB-rich domains are dispersed in the matrix of PS-rich phase even at the 5CB content of 80%. A strong dielectric relaxation due to rotation of the 5CB molecules in the isotropic PS-rich phase has been termed alpha. The alpha process exhibits complex temperature dependence due to the changes in the composition and morphology with temperature. Although the 5CB-rich phase crystallizes mostly at low temperatures, some 5CB-rich droplets of a small size remain without crystallization and exhibit dielectric relaxations termed beta and gamma. The beta and gamma processes are assigned to rotation of the 5CB molecules around the short and long axes of the rodlike 5CB molecule, respectively. Besides those dipolar relaxation processes, a relaxation termed alpha' is observed at PS/5CB compositions of 5/5 and 4/6 and assigned to the Maxwell-Wagner effect.