Laravel 5.x is, for many, the Go To MVC framework and on balance we would agree. It is a robust product in every sense and without any client preference we would choose Laravel. This particular web-site is written in Laravel, albeit this is not a particularly complex site from a Laravel point of view.
Given the popularity of Laravel and its community, it is both a wise and effective framework to use for your App. It is currently the #1 framework in use right now and as a result it is very well supported by most agencies and almost all contractors.
It's also worth noting that Laravel's very recent versions require PHP 7.2 [Nov 2017] as does the new CI4, so it's possibly worth double checking that is OK [no reason why not].
We have some `proper` Laravel stuff with CMS, MySQL and AJAX etc. so if you'd like to see more then just ask.