Messages told be I needed to use iNessage, but there is no APL with that name in the App Store!Help!

The app on your phone is called “Messages”. You can use it to send both SMS (standard text) messages and iMessages. “iMessages” is an Apple messaging service.

Start here:

Use iMessage apps on your iPhone, iPad, and iPod touch - Apple Support

If you actually mean something called “iNessage”, I don’t know how to help you.

iMessage is one name for the built-in Apple Messages app. It is part of iOS.

The iOS version shown in your footer is old. An iPhone 5s can get to iOS 12 (12.5.x) which is still very old, but less old. Here is how to update an iPhone: Update iOS on iPhone - Apple Support

Learning still wrote:

Hmmm. I have an iPhone 12Pro and version 16.2, so not sure where you got your info.

Where? From the footer shown in your posting. This footer is usually selected when the question is posted.