What version of IOS are you running? You can find out in Settings > About.
The version requirements stated in the app store are usually minimum requirements. They are not specific. In other words, that app is unlikely to be only for version 5.1. It is for all versions 5.1 and above, which hopefully applies to you.
If you are running something before 5.1 then you should probably update the device unless you have a good reason not to want to (such as maintaining a jailbreak or an aversion to IOS 6).