Since you are asking specifically for iOS 5.1.1, you are likely trying to run Netflix on an older device (like the original iPad, iPhone 3GS, or iPod Touch 3rd/4th Gen).
To bypass this, many users rely on the "Purchased" tab workaround: The Shared Apple ID netflix ipa ios 5.1.1
For devices running iOS 5.1.1 (like the 1st generation iPad), the official Netflix (v4.3.1) is the last compatible version available. Because the current App Store version requires much newer software, you typically cannot download it directly through a standard search. Recommended Installation Methods Since you are asking specifically for iOS 5
In theory, the App Store should offer you Netflix 6.x or 7.x – the final builds that supported iOS 5.1.1. In theory. Server-Side Cutoff: Netflix
How to Install Any App on iOS 5.1.1 or Older - (ipad First Gen)
Download Compatible Version: Find Netflix in the list and tap the Cloud icon. You should see a prompt: "Download an older version of this application?" Tap Download. Where to Find a Netflix IPA (Archive)