Look at the documentation at www.Laravel.com it has extensive information about how to upgrade from one version to the next.

If you want to be sure then:

• Upgrade from 5.5 to 5.6
• Upgrade from 5.6 to 5.7

There are no breaking changes in minor versions, in fact it should do that upgrade itself if you run composer update (remember this is how you upgrade locally on the development machine, and that the command on the server is composer install --no-dev)

Feel free to ask me questions about Laravel. I have worked extensively full time on it for 5 years :-)

I can't speak for the specifics from 5.5 to 5.5.42 but the latest version is 5.7 - so perhaps upgrade to that instead. It comes with significant performance improvements as well as changing a few significant things. Check the docs :)
laravel.com/docs/5.7

I am not sure about laravel maybe there is an artisan outside who is qualified.

but since they use a semver pattern for versioning and they are a dominant framework:

• there should be no breaking changes in the interface in a minor update
• there should be no problems with the update
• all versions 5.x.x should be compatible on an interface level with each other

there are however tools, Tomáš Votruba, a really nice guy from czech wrote an auto upgrade tool: github.com/rectorphp/rector

which refactors a lot of the code of most frameworks automatically. You just need to check if he supports laravel.