iPhone Ios 5.1.1

That isn't possible as far as I know
In the past I've got moderate success with some apps by modifying the iOS version using iFile but it was on my 3G which supports up to 4.2.1 and I changed it to 4.3, I don't know what kind of errors you might get by making such a big change.
it might help reading this thread
You're either stuck with 5.1.1 or 7 since SHSH blobs don't allow restores on the 4S

No.
There is modules there missing that iOS 5 does not have and the app might call for.
Even if you tricked the iOS version your iPhone can get stuck and will need a restore if you install an app not compatible with your firmware version.

Wasn't the App Store now supposed to support older versions of Apps ie. if you have an older device or an older operating system it would let you download the latest version of the app that was compatible with your iOS??

http://9to5mac.com/2013/09/17/ios-a...loads-to-support-older-hardware-and-software/

braxton34 said:

Wasn't the App Store now supposed to support older versions of Apps ie. if you have an older device or an older operating system it would let you download the latest version of the app that was compatible with your iOS??

http://9to5mac.com/2013/09/17/ios-a...loads-to-support-older-hardware-and-software/

Click to expand...

For most apps, yes. I noticed that some apps, such as dataman, do not let you

I was running iOS 6 and I must've installed it in the past since there was a cloud but when I tried to install it, it told me that I needed iOS 7 without letting me install the iOS 6 version

I am also on iOS 5.1.1 and have same issues. Although app store does allow older versions, but some apps play dirty like Fleksy. It refuses to work unless i update it.