The Facebook Messenger app is compatible with iOS 9.3.5, but with some limitations. According to Apple's App Store, Messenger requires iOS 10 or later to run. However, some users have reported that they can still download and install older versions of Messenger that support iOS 9.3.5.
To download Messenger on a device running iOS 9.3.5, you must use a workaround
Are you trying to install this on a specific device, like an or an iPhone 4s ?
If the app remains unstable, many users on iOS 9.3.5 resort to using the mobile browser.