Emerging 5G millimeter-wave (mm-wave) networks use electronic beamforming and beamsteering and support signal bandwidths on the order of hundreds of MHz. Given these characteristics, opportunities exist to develop 3-D sensing applications that leverage 5G mm-wave communications infrastructure. In this context, this work introduces a signal processing pipeline that can: 1) accurately extract the Time of Flight (ToF) of reflected orthogonal frequency division multiplexing (OFDM) communications signals and 2) enhance range resolution by coherently aggregating the reflection information from separate frequency bands. In combination with precise beamsteering, the proposed signal processing techniques enable high-resolution 3-D radar imaging without affecting communications protocols. An experimental system demonstrating this concept has been implemented and is described. This system consists of two software-defined phased array radios (SDPARs), one configured as a prototype 5G base station TX, and one as an auxiliary prototype 5G RX. Each SDPAR primarily consists of a Si-based 28-GHz, 64-element, phased array transceiver module and software-defined radio. Simulation and benchmark results show that our coherent bandwidth stitching enables accurate OFDM-based ranging with 15-cm resolution. Measurement results show 3-D radar images of indoor scenes with 2° angular and 15-cm ranging resolution, created by processing reflected 5G-like communication waveforms at 28 GHz. The produced 3-D radar images effectively depict the location of objects in the scene, and these locations are in close agreement with the ground truth.