Over-the-air federated learning (OTA-FL) offers an exciting new direction over classical FL by averaging model weights using the physics of analog signal propagation. Since each participant broadcasts its model weights concurrently in time and frequency, this paradigm conserves communication bandwidth and model upload latency. Despite its potential, there is no prior large-scale demonstration on a real-world experimental platform. This paper proves for the first time that OTA-FL can be deployed in a cellular network setting within the constraints of a 5G compliant waveform. To achieve this, we identify challenges caused by multi-path fading effects, thermal noise at the radio devices, and maintaining highly precise synchronization across multiple clients to perform coherent OTA combining. To address these challenges, we propose a unified framework for real-time channel estimation, model weight to OFDM symbol mapping and dual-layer synchronization interface to perform OTA model training. We experimentally validate OTA-FL using two relevant applications - Channel Estimation and Object Classification, at a large-scale on ORBIT Testbed and a portable setup respectively, along with analyzing the benefits from the perspective of a telecom operator. Under specific experimental conditions, OTA-FL achieves equivalent model performance, supplemented with 43 times improvement in spectrum utilization and 7 times improvement in energy efficiency over classical FL when considering 5 nodes.