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Internal server errors (errors 5xx) are often caused by plugin or theme function conflicts, so if you have access to your admin panel, try deactivating all plugins, to define source of the troubles. If you do not have access to your site wp admin panel, try manually reset the plugins (no Dashboard access required): by ftp rename folder wp-content/plugins, refresh any site page, rename the folder back to the plugins. If that resolves the issue, enable each one by one until you find the issue.
If that not resolved the issue, try switching to the default wordpress theme to rule-out a theme-specific issue. If you do not have access to your admin panel, access your server trought FTP, or a file manager in your hosting account control panel, navigate to /wp-content/themes/ and rename the directory of your currently active theme. This will enable the default theme and will show is the issue is there.
If that not resolved the issue, it is possible that .htaccess file rule could be the source of the problem. To check for this use FTP client or the file manager on your hosting account panel, then rename the .htaccess file. If you can not find the .htaccess file, make sure that you have set your FTP client to view invisible files.
If you were not able to resolve the issue by either resetting your plugins and theme or renaming your .htaccess file, ask help to your site developers, but they will need a more detailed error message. Internal server errors are described in more detail in the server error log. If you have access to the server error log file - generate the error again, note the date and time, then check your server error log file for any errors that occurred during noted time period. If you do not have access to the server error log file - ask your hosting provider to help you with it.
Also you can use more advanced way to do tests of the site - in 99% it will help.
Also we reccomend plugin Error Log Monitor for your site, which will informate you about any issues after the site update, and which also make log file of the issues