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Proliferation of 5G devices and services has driven the demand for wide-scale enhancements ranging from data rate, reliability, and compatibility to sustain the ever increasing growth of the telecommunication industry. In this regard, this work investigates how machine learning technology can improve the performance of 5G cell and beam index search in practice. The cell search is an essential function for a User Equipment (UE) to be initially associated with a base station, and is also important to further maintain the wireless connection. Unlike the former generation cellular systems, the 5G UE faces with an additional challenge to detect suitable beams as well as the cell identities in the cell search procedures. Herein, we propose and implement new channel-learning schemes to enhance the performance of 5G beam index detection. The salient point lies in the use of machine learning models and softwarization for practical implementations in a system level. We develop the proposed channel-learning scheme including algorithmic procedures and corroborative system structure for efficient beam index detection. We also implement a real-time operating 5G testbed based on the off-the-shelf Software Defined Radio (SDR) platform and conduct intensive experiments with commercial 5G base stations. The experimental results indicate that the proposed channel-learning schemes outperform the conventional correlation-based scheme in real 5G channel environments.