What music and texting apps can iPhone 5 support?

The Apple Messages app is at least for now, compatible with an iPhone 5. It requires iOS 10, which is an iOS version compatible with iPhone 5. Apple Music is the same. It requires iOS 10 at this time.

At some point however, an iPhone 5 won't work with very many apps out there. You can't run YouTube or Netflix on one for example.

The iphone 5 is obsolete. You will find few, if any apps of any kind that are available for it.

In many countries, including the US, it is not even useful as a basic phone any more as it does not meet the minimum requirements set by the cellular network providers.