It is possible, a bit tricky, but possible. First, you'll need to download the Whatsapp app through iTunes on your computer, this will make it show up as "purchased" in your library.
After that, open up the App Store on your iPhone and go to the 'purchased' tab. When you try to install it this way it will tell you that you need iOS 6 or higher, but will also ask if you would like to download an older version of the app. then click on download.
- again step by step:
1) Open up iTunes on your computer
2) Go to Store (left hand column) ->iTunes Store
3) Search for Whatsapp; - download the app
4) then open App Store on your iPhone
5) Click on 'Purchased'
- you will have to install Whatsapp by clicking on it as usual.
App Store will ask you: "Download an older version of this app. The current version requires iOS 6.0 or later, but you can download the last compatible version.",
- then click on Download and it should finally work.