Custom error/fatal error and exception handler in PHP
The first thing which comes to my mind when reading your code is how concurrent requests with errors can tamper with the written data. You can aqquire an exclusive lock on the file for the duration of the writing with the flag LOCK_EX (see file_put_contents documentation).

I would also make sure the file 500.php actually exists. You could also avoid using require_once since the script is terminated afterwards and the possibility for another include is non-existent.

I assume the comments are because the code is posted here, since none of them provide extra information your code doesn't provide. Otherwise I think your code look fine. The variables have meaningful names and the indentation is good.

Happy coding!