The 5G approximately provides 1000x higher mobile data traffic and 10 to 100x numbers of connected devices than the 4G. The 5G is becoming a reality after deploying it by some of the main cities in the world. Millimeterwave (mm-wave) communications play a crucial role in the 5G networks owing to its enormous available bandwidth. The hybrid beamforming (HBF) presents better multiplexing gains than analog beamforming. It is a trade-off between cost and performance. As a result, the HBF is a promising approach that exploits the small digital beamforming and the high analog beamforming to meet these challenges. This study proposes and simulates a limited feedback hybrid beamforming for outdoor environments, including the analog precoding/combining based on a quantization codebook and the digital precoding based on Lagrangian optimization with the mathematical model in detail compared with other algorithms in the literature. It achieves an increase in the spectral efficiency satisfied, such as at 20dB SNR, it is approximately 11.75 bps/Hz while the other solutions are 11.18, 11.4, and 11.8 bps/Hz. Also, it presents work well in all possible and satisfies the quality of the results for all cases, such as increasing the number of users, number of multi-path, the SNR, and the BS antennas. Also, it offers the BER approximately 10 -4 at 10.3 SNR, better than other solutions.