What is the best way to upgrade Laravel live project?

I just joined company where has a big project on the live server which needs to implement new functionality. But the problem that it's running on PHP 5 and Laravel 5. I think before expanding functionality I have to update it to the newest version of Laravel and finally update it to PHP 7. What is the best way to do it? Try to set it up locally and go from there? Or better to use docker? Maybe anybody has some tips on what I should have in mind while updating Laravel versions? As I know everything is in the documentation and you have to update it one by one. For example from Laravel 5 to Laravel 5.1 and so on.

Thank you for your help

via Chebli Mohamed