iOS 5.1.1 is the last software update that the iPad 1 received. You can't update to a later version, such as iOS 8.
Every other iPad, starting from the iPad 2 up to the iPad Air 2, are receiving the most recent software, which is iOS 9.0.2 at the moment.
If the app only works with a software later than 5.1.1, you'll need to get an iPad different than the iPad 1.