The energy consumption of the fifth generation(5G) of mobile networks is one of the major concerns of the telecom industry. However, there is not currently an accurate and tractable approach to evaluate 5G base stations (BSs) power consumption. In this article, we propose a novel model for a realistic characterisation of the power consumption of 5G multi-carrier BSs, which builds on a large data collection campaign. At first, we define a machine learning architecture that allows modelling multiple 5G BS products. Then, we exploit the knowledge gathered by this framework to derive a realistic and analytically tractable power consumption model, which can help driving both theoretical analyses as well as feature standardisation, development and optimisation frameworks. Notably, we demonstrate that such model has high precision, and it is able of capturing the benefits of energy saving mechanisms. We believe this analytical model represents a fundamental tool for understanding 5G BSs power consumption, and accurately optimising the network energy efficiency.