When you configure a cache in Edge you give it some key fragments (e.g. request.uri, request.header.Accept, request.header.Accept-Language, etc.). To clear that key you pass the same key fragments.
If I have 5,000 elements cached, how can I clear the entire cache without generating 5,000 calls to my API with all the possible cache keys?
You can use the clear all cache entries API call, documented here. If you don't pass in the prefix query parameter, it should remove all.