Channel-state information (CSI)-based sensing will play a key role in future cellular systems. However, no CSI dataset has been published from a real-world 5G NR system that facilitates the development and validation of suitable sensing algorithms. To close this gap, we publish three real-world wideband multi-antenna multi-open RAN radio unit (O-RU) CSI datasets from the 5G NR uplink channel: an indoor lab/office room dataset, an outdoor campus courtyard dataset, and a device classification dataset with six commercial-off-the-shelf (COTS) user equipments (UEs). These datasets have been recorded using a software-defined 5G NR testbed based on NVIDIA Aerial RAN CoLab Over-the-Air (ARC-OTA) with COTS hardware, which we have deployed at ETH Zurich. We demonstrate the utility of these datasets for three CSI-based sensing tasks: neural UE positioning, channel charting in real-world coordinates, and closed-set device classification. For all these tasks, our results show high accuracy: neural UE positioning achieves 0.6cm (indoor) and 5.7cm (outdoor) mean absolute error, channel charting in real-world coordinates achieves 73cm mean absolute error (outdoor), and device classification achieves 99% (same day) and 95% (next day) accuracy. The CSI datasets, ground-truth UE position labels, CSI features, and simulation code are publicly available at https://caez.ethz.ch