Matt Stauffer has posted a guide to his site to help you migrate from Laravel 4 to Laravel 5 as painlessly as possible. This is part fourteen in his overall introduction to Laravel 5 series of posts.
It's very simple to get started in a new Laravel 5 app [...] but what if you have a Laravel 4 app you want to upgrade? You might think the answer is to upgrade the Composer dependencies and then manually make the changes. Quite a few folks have created walkthroughs for that process, and it's possible—but there are a lot of little pieces you need to catch, and Taylor has said publicly that he thinks the better process is actually to start from scratch and copy your code in. So, that's what we're going to be doing.
He walks you through cloning a new Laravel 5 instance and setting up the various pieces of the application including the app itself, the domain folder and Composer dependencies. He then gets into the migration of things in the "app/" folder like controllers, database migrations and models. He also includes steps to update namespacing, handling the configuration updates, moving over user handling and any forms you may have created.