I have an iPad Air late 2013 with iOS 12.5.5 and I need to update the iOS, but the iPad and my Mac say that 12.5.5 is the latest iOS version, yet there are streaming services that no longer work due to the iOS version being so old.

An original iPad Air from 2013, which was released now 9 years ago, is simply too old, too underpowered and simply not capable of being updated past iOS 12.5.5. If you need the newer iPadOS versions, as I can well imagine you do, it is now time to retire your now obsolete iPad in favor of a newer, more modern iPad.

Not the news you hoped for, I'm sure. But fact none-the-less. You may get other much longer responses, but this short response is really what you need to understand.

Insofar as your iPad is capable, its system software is up to date. The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.5.

Apple ended major update support for these models of iPad in September 2019 - although they since continue to receive occasional “point” security updates - the most recent being released late last year. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.

Some App developers have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions). 

Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS15.

Sorry, I appreciate that this may not be what you were hoping to learn.

I hope this information provides clarity as to your available options - and the fundamental limitations of your iPad.

Perhaps to invest in a newer iOS device may resolve this issue.

As those age they only lose compatibility with newer tech. 😸🐾

You're welcome and good luck.