"Unable to Download App" on iOS 7.1.1
Luckily, I could fix my issue. 

I had to change my DNS to 8.8.8.8. 
My internet used to work before this but after changing my DNS now I am able to download apps from App Store. 

But I tell I haven't changed any setting on my iPad 2 running iOS 6 still every thing works including App Store downloads. I think this issue is with iPhone 5 or definitely iOS 7.1.1.