Here is the good news that many users miss: Apple implemented a feature specifically for this scenario.

The prospect of downloading Facebook on an iPad running iOS 5.1.1 is more than a technical hurdle; it is a journey into the "digital afterlife" of early mobile computing. Released in 2012, iOS 5.1.1 represents the final frontier for the original iPad and a specific era of the mobile web. Today, attempting to install the modern Facebook app on such a device is a lesson in software obsolescence and the evolving nature of social connectivity. The Barrier of Version Incompatibility