I had the same problem but was able to resolve it with technical info from Apple Customer Service.
The solution is to delete the ibooks 3.2 app from your itunes on your Mac computer (and iPad), then replace the 3.2 version using the older version of ibooks which is 3.1.1.ipa.
It is not easy to find an older version of ibooks because Apple doesn't seem to make it available it, but there are a couple of sites out there that have it if you seach for "ibooks 3.1.1.ipa download".
The site I found it on was: http://zonatrick.com/apps-games/download/mobile/UKjR0LcH/iBooks_311.htm.
After searching, I confirm Agility solution, the easiest way to install ibooks on IOS 5.1.1:
1. download the latest version of Ibooks in Itunes (i.e. version 3.2)
2. synch with your Ipad/etc..
3. go in purchased items on your ipad and begin to install ibooks, it will then tell you that it is compatible with ios 7 only, BUT that you can try to download the latest version available for your IOS. It will then install Ibooks version 3.1.3
4. after installing it on you Ipad, delete the ibooks 3.2 app from your itunes, it will not remove ibooks from your Ipad, but you will avoid the nasty message (ibooks 3.2 is not compatible with your version of IOS) each time you synch...