500 Server error messages tend to be the result of a misconfiguration in the HTTP server, a common example is with a problem in a .htaccess file on Apache for example.
If you have access to server error logs then you might want to take a look and see if there is an error showing in the logs.
If that is no joy, then you might want to temporarily rename your htaccess file if you are using Apache to .htaccessold. If using an FTP client you may have to flag, show hidden files. If that let's you get into the admin area, then go to Settings Permalinks to generate a new htaccess file.
Failing all that, try contacting your host, as their may genuinely be an issue with the server.