Inorder to support our apps in the latest version of iOS we can only support devices running iOS 6 and newer. This is based on Apple's choice to drop support for these older devices within the latest version of their developer tools. You will probably run into this issue with other apps unfortunately.
When iTunes installs an app from the store it adds a special key that allows your device to open it. Which is why we cannot just send the old version out to players. Only apps which are installed from the store can run on your device. You either have to restore your device from a recent iTunes backup from before you deleted the app or, if you have an older version of the app downloaded in iTunes you can reinstall that onto your device.
Please see the following link for more info on restoring from backup: http://support.apple.com/kb/ht1766