My father in law is considering getting an iPhone 5. There are some specific apps that he is interested in; are all apps available for iPhone 4 also available for iPhone 5, or do developers have to port them?
All for previous iPhone and iPod touch devices will run, but won't necessarily be optimized for the larger screen. If that's the case, the app will run at the previous (3.5" size) with a black bar above and below the app's content.
It is far, far more common for a developer to specify that an application needs a minimum iOS level as opposed to not being available on a specific device.
For the applications that are available only for some devices, the most common (by far) restriction is that they test for new hardware and refuse to run on an older device. If an application needed multiple microphones to do noise cancelling, one would presume that it might not install or run on an older iPhone that had only one microphone.
In your case - apps purchased and running on an old phone are almost certainly going to run on newer hardware. The worst that would happen is that the app wouldn't take use of the entire larger screen and only draw itself centered using most of the iPhone 5's slightly taller screen.