Localization inside legacy private 5G networks is a daunting task that involves solving the problem of indoor localization using commercial off-the-shelf proprietary hardware. While some previous work has focused on experimental analysis, none has undertaken to develop a realistic solution based on commercial equipment. In this study, we present the first comprehensive and concrete 5G framework that combines fingerprinting with the 3GPP Enhanced Cell ID (E-CID) approach. Our methodology consists of a machine-learning model to deduce the user's position by comparing the signal strength received from the User Equipment (UE) with a reference radio power map. To achieve this, the 3GPP protocols and functions are improved to provide open, centralized, and universal localization functions. A new reference map paradigm named Optical Radio Power Estimation using Light Analysis (ORPELA) is introduced. Real-world experiments prove that it is reproducible and more accurate than state-of-the-art radio-planning software. Machine-learning models are then designed, trained, and optimized for an ultra-challenging radio context. Finally, a large-scale experimental campaign encompassing a wide range of cases, including line-of-sight or mobility, is being conducted to demonstrate expected location performance within realistic 5G private networks.