My iPad is still on 12.5.5 and says it is up to date. Is there an update available for iPad mini 3 please?

Hello ~ No …your iPad mini 3 cannot be updated any further. You need a newer device in order to use a higher version of iOS. Go to upper left click on the two lines then iPad to see newer options. Also if considering a second hand device please take a moment to read these…

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Also:

The All Too Common SAD Reality of Buying a Used iPad/iPhone

~Katana-San~

Hi, iPad Mini 3 has iOS 12 as latest OS available.

Latest release of iOS 12 is iOS 12.5.5, About iOS 12 Updates - Apple Support, link show all updates and the last one is the latest available.

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 continued to receive occasional “point” security updates until 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 capabilities and available 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.

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