Real-time audio-visual speech enhancement (AVSE) is a key enabler for immersive and interactive multimedia services, yet its performance is tightly constrained by network latency, uplink capacity, and computational delay. This paper presents the design, deployment, and evaluation of a complete cloud-edge-assisted AVSE system operating over a public 5G edge network. The system integrates CNN-based acoustic enhancement and OpenCV-based facial feature extraction with an LSTM fusion network to preserve temporal coherence, and is deployed on a Vodafone-compatible AWS Wavelength edge cloud. Through extensive stress testing, we analyze end-to-end performance under varying network load and adaptive multimedia profiles. Results show that compute placement at the network edge is critical for meeting real-time coherence constraints, and that uplink capacity is often the dominant bottleneck for interactive AVSE services. Only 5G and wired Ethernet consistently satisfied the required communication delay bound for uncompressed audio-video chunks, while aggressive compression reduced payload sizes by up to 80% with negligible perceptual degradation, enabling robust operation under constrained conditions. We further demonstrate a fundamental trade-off between processing latency and enhancement quality, where reduced model complexity lowers delay but degrades reconstruction performance in low-SNR scenarios. Our findings indicate that public 5G edge environments can sustain real-time, interactive AVSE workloads when network and compute resources are carefully orchestrated, although performance margins remain tighter than in dedicated infrastructures. The architectural insights derived from this study provide practical guidelines for the design of delay-sensitive multimedia and perceptual enhancement services on emerging 5G edge-cloud platforms.