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The 5xx series of status codes is for representing problems on the server side. In most cases, these codes mean the server is not in a state to run the client’s request or even see whether it’s correct, and that the client should retry its request later. Sometimes the server can estimate how much later the client should retry its request, and put that information into the Retry-After response header.
There are fewer 5xx status codes than 4xx status codes, not because fewer things might go wrong on the server, but because there’s not much point in being specific: the client can’t do anything to fix a problem on the server.