How to get a Custom 500 Error Page to show?

Does wordpress have any built-in settings for doing this?

Most likely your host will have an option on your cPanel for custom Error pages. Something along the lines of:

Custom error pages

If that is not the case, please have a look at this older question:
How to create custom 401, 403 and 500 error pages?

EDIT 1:
Also at this one: https://stackoverflow.com/questions/12184402/wordpress-how-to-add-a-custom-500-server-error-page

EDIT 2:
You can also try this Gist as an alternative. Instead of using the .htaccess file, you can place the code in your functions.php

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