It can be a false expectation, but it should not be. I think that when 5xx errors happen the logging/alerting system should notify the developers/support/infra

It can be a false expectation, but it should not be. I think that when 5xx errors happen the logging/alerting system should notify the developers/support/infra teams. So, somebody should start working on it ASAP, or whatever your SLA target is. It is definitely true, though, that the user can't do anything to fix it. They just have to try again later. All this, of course, assumes that the code is returning proper error codes, which might also be a false assumption :)