500 internal server error is most critical error for any websites so on for WordPress too. It is critical because this error not happen only for 1 or 2 reason but for some unknown reason too. So before talking about solutions we must have to find out what causing this error. Here is some check list which you can try to find out why this is happening and what to do then.
Where to start?
First check your .htaccess file, connect your site using FTP client then rename .htaccess file to something else, now go back to your site and hard refresh it by ctrl+f5 key on your keyboard or delete your browser cache. If 500 internal error disappear then do not use old renamed .htaccess again, upload fresh copy of your .htaccess file so 500 error should go permanently. If you need WordPress default .htaccess code see here.
.Htaccess file ok but still have the error?
If you are on VPS then think what changes you have made recently on your server, if you edited php.ini, httpd.conf or nginx.conf files then roll back those changes then check the result.
If you are on shared hosting plan then look into cPanel>php configuration and increase your memory limit to minimum 256MB or 512MB and and also increase Max execution time to 90 or to 300, now save and delete your browser cache then check if your 500 internal server gone or still there. If it is still there then contact your hosting service provider so they can take a look and give you suggestions on what to do or solve it for you.