Centralized cloud computing with 100+ milliseconds network latencies cannot meet the tens of milliseconds to sub-millisecond response times required for emerging 5G applications like autonomous driving, smart manufacturing, tactile internet, and augmented or virtual reality. We describe a new, dynamic runtime that enables such applications to make effective use of a 5G network, computing at the edge of this network, and resources in the centralized cloud, at all times. Our runtime continuously monitors the interaction among the microservices, estimates the data produced and exchanged among the microservices, and uses a novel graph min-cut algorithm to dynamically map the microservices to the edge or the cloud to satisfy application-specific response times. Our runtime also handles temporary network partitions, and maintains data consistency across the distributed fabric by using microservice proxies to reduce WAN bandwidth by an order of magnitude, all in an {\it application-specific manner} by leveraging knowledge about the application's functions, latency-critical pipelines and intermediate data. We illustrate the use of our runtime by successfully mapping two complex, representative real-world video analytics applications to the AWS/Verizon Wavelength edge-cloud architecture, and improving application response times by 2x when compared with a static edge-cloud implementation.