CODETutorial has a good tutorial on how to use Laravel 5 API basic authentication.

In this tutorial we will see how to use Laravel 5 to serve as a REST API backend implementing also a simple basic HTTP Authentication to store data for different users of the application. We will use a middleware to provide the authentication for the REST call. This middleware will authorize the user at every request without storing info about session or using token.

Laravel REST API Basic Authentication

Wanna learn more about developing APIs in Laravel 5? Check out our Laravel 5 Cookbook.