For apps that have the pre-requisite of iOS 6.0 and above (does not apply for iOS 7.0 and above), if you must, there is a way to circumvent the pre-requisite and still install the app. Note that this is unstable and often not recommended because there may be API differences that the app is calling on, hence the iOS 6.0+ requirement. But for iOS 6.0+ apps, mostly it's a system requirement, not much so a software requirement, so even if you circumvent it, it will not cause harm to your device assuming it's an Apple AppStore official app (this cannot be said for Cydia packages as circumventing for packages should NEVER be done).
But in essence, if you really need to use an iOS 6.0+ requiring application from the AppStore and is mandatory that you use it, then we can circumvent the pre-requisite (without resorting to piracy as many users will suggest on other sites/forums).
On the note of iOS 7.0+ requiring apps, it's recommended that you do not circumvent them because if the app is requiring iOS 7.0+, it most likely does not use residual APIs from the <iOS 6 era, and installing such apps will most likely result in a boot loop, meaning you'd end up crashing often and probably boot looping, so you'd have to restore frequently, making it impractical.