There are a few ways to do this:
1. Use HTTP or HTTPS (depending on your site) and match on a 500 response code specifically. When creating either of these monitors, in the section "Match string or regular expression" you would enter the response code and string, i.e. 503 unavailable.
To be alerted if an HTTP response code, such as 500, appears on the page, enter the following into the section "Match string or regular expression"
!/500 internal error/
2. Or also use a script monitor and use JMeter to look for a 500 error code. The script will also be more beneficial in that you could code it to catch more response codes such as 404, 503, etc....