Complete rewrite:
From Laravel 5.1 to Laravel 6 there are a lot of breaking changes, including the supported PHP versions and the functions you probably used to implement the platform.
I had to do such an upgrade and decided to just rewrite the application from scratch. I was way more efficient compared to having to upgrade from version to version until I get to the desired Version.
It still depends on the size of your application.
If a rewrite is not an option:
You have to go from one version to another, until you reach the desired version. I would recommend going through the upgrading to v x.x page (for example https://laravel.com/docs/5.2/upgrade#upgrade-5.2.0) of each version and see what has changed.
Commercial Alternative:
You can consider using a pretty affordable service such as Laravel Shift to shift from one version to another seamlessly. Check it out! https://laravelshift.com/