I guess you are referring to the iPad mini 1st generation, The iPad 1st generation and its older iOS (5.1.1), is no longer supported. The Apple store provides the latest version that requires iOS 10. If your iPad can run no greater than iOS 9.3.5, I believe you need to attempt to queue the older download from the App Store in iTunes (try to remove/add it again, if it is already present).

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You can try this with the iPad mini synced or if the same Apple ID is used, after re-adding it iTunes, you can try to add it again from the store on the iPad and it might prompt/allow you to install a supported older version.