5G and future cellular networks intend to incorporate low earth orbit (LEO) satellite communication systems (SatCom) to solve the coverage and availability problems that cannot be addressed by satellite-based or ground-based infrastructure alone. This integration of terrestrial and non terrestrial networks poses many technical challenges which need to be identified and addressed. To this aim, we design and simulate the downlink of a LEO SatCom compatible with 5G NR, with a special focus on the design of the beamforming codebook at the satellite side. The performance of this approach is evaluated for the link between a LEO satellite and a mobile terminal in the Ku band, assuming a realistic channel model and commercial antenna array designs, both at the satellite and the terminal. Simulation results provide insights on open research challenges related to analog codebook design and hybrid beamforming strategies, requirements of the antenna terminals to provide a given SNR, or required beam reconfiguration capabilities among others.