Newer versions of Acrobat Reader for iOS will not run on iOS 5.1.1. However, you can download and install the latest compatible version of Reader for iOS from the App Store.
Would you please take look at the following forum threads to see if it works for you?
The same steps described in the forum threads should work for the first generation of iPad running iOS 5.1.1, for example The latest compatible version of Reader is 11.0.1.
Please let us know if you have additional questions.