Earlier quoted context omitted.
PHP 5 has been deprecated for several years now. PHP 7.0 was released in 2015, almost five years ago. The current version is PHP 7.3. While upgrading from PHP 5.4 or lower to 7 can be... interesting, it's not all that difficult or time-consuming. PHP 5.5 or higher to 7 is much easier.
We personally struggle to just keep Ubuntu updated with LTS releases, let alone managing all the updates to ensure software works on the new packages installed on whatever LTS version. The issue is that when you have smaller companies with small web development departments you end up with a lot of differents sites/tools made over time. So now when it comes upgrade time you have a large pile of stuff that needs upgrad…
If the business decides the risk is acceptable, then that's fine. As an engineer, you're supposed to communicate and document the risks associated with technical decisions. After that, if your employer decides Technology X.Y is good enough, then accept it and move on. You made your case, and the business considered it and made a choice.