We report on experimental results on the use of a learning-based approach to\ninfer the location of a mobile user of a cellular network within a cell, for a\n5G-type Massive multiple input, multiple output (MIMO) system. We describe how\nthe sample spatial covariance matrix computed from the CSI can be used as the\ninput to a learning algorithm which attempts to relate it to user location. We\ndiscuss several learning approaches, and analyze in depth the application of\nextreme learning machines, for which theoretical approximate performance\nbenchmarks are available, to the localization problem. We validate the proposed\napproach using experimental data collected on a Huawei 5G testbed, provide some\nperformance and robustness benchmarks, and discuss practical issues related to\nthe deployment of such a technique in 5G networks.\n