Hi Vicky!
Look in your template's folder for the error.php file. This is called whenever Joomla tries to deal with an application-level error, including 404 Not Found errors. This is the one crashing with a 500 Internal Server Error. For example, if your template is EXAMPLE you should look into <site root>/templates/EXAMPLE/error.php because that's the file that's really crashing.
But wait, how is it even possible that trying to access a non-existent image trigger Joomla's error page? That's because since Joomla 3.3 the .htaccess shipped with it is designed to catch all non-existent files / links and route them to Joomla. Of course Admin Tools' .htaccess Maker had also been updated to create the same kind of basic code.
Why would it do that? Because that's how SEF URLs work! When you type, say, https://www.akeebabackup.com/download/admintools/5-0-1.html, there is no "download/admintools" folder structure on our site's disk, let alone a file called 5-0-1.html. What happens is that this is a "not found" URL. The .htaccess tells Apache to route this through Joomla's index.php file. Joomla's SEF router sees the path of the request (download/admintools/5-0-1.html) and processes it by figuring out menu item structure and calling the relevant component. Had it not found the relevant menu item or otherwise didn't understand what to do with it, Joomla would raise a 404 Not Found exception which results in the template's error.php file being called to render it.
So how come your other sites don't crash? You're using a different -or updated- template :) For what it's worth, we've seen the faulty error.php file on quite a lot of well-known template clubs' older templates. This is the file that very few people test. I know because ours was a bit of a mess, with 60pt text until I spent an evening giving it the time, love and care it deserved a full two years after I had launched the previous iteration of our site :D
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!