It's simpler to try another web browser. If the site fails it's clear they have issues. See if it is working in Google Chrome or Firefox etc.
A 500 error is an 'internal server error', so the site in question really should look at their own server logs (give them a time & your timezone that the errors occured).
https://en.wikipedia.org/wiki/List_of_HTTP_status_codes
It's obviously bad if a visitor can crash their server.
You can check Safari's extensions are all up to date (assuming you have some installed) by looking in the Safari Preferences.
You can also use Safari's 'private browsing mode' (in the Safari menu) to prevent any login cookies causing issues, see if that makes a difference.
It is also possible to reset Safari & empty it's caches. That will obviously lose all of your browsing history, login cookies, download history etc, so take care to only select items that you are comfortable loosing.
You can also test in a completly new user account to see if only your account is affected. Create one in 'System Preferences > Users & groups' (call it test). Login as test & see if the error still appears in Safari.