My 5th generation iPad won't show me any updates past 12.3.1

Whether or not you are able to update any iPad to a newer version of iOS/iPadOS will be dictated by the iPad model - and the currently installed version of iOS. You can find this information here:

Settings > General > About

Not sure which iPad you have? Identify your iPad model.

Here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:

32-bit devices (obsolete)

iPad1 - iOS 5.1.1

iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)

iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)

64-bit devices

iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.6

iPad Air2, iPad mini4 - iPadOS 15.7.1

Newer models are all able to be updated to the current version, iPadOS 16.1.1

• iPad Pro (all models)
• iPad Air (3rd generation and later)
• iPad (5th generation and later)
• iPad mini (5th generation and later)

If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

Be aware that while an iPad may be capable of update, it may be too far behind the current version to be updated directly from iPad settings. In such circumstances you will likely need to use a computer to perform the update. You will need access to either a Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:

How to uninstall iOS beta software - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

Ok, if the update is not showing up wirelessly then you may need to use a comptuter.

at the link is another link to instructions based on the computer you have to use (mac vs PC)

if you don’t have a computer that can run iTunes you may need to borrow a friend’s or make an appointment at an Apple Store or authorized service provider for them to help you

Update your iPhone or iPad - Apple Support

Make sure your iPad has no VPN running. If it does, temporarily, disable it.

Make sure your iPad is not running any test, Beta iOS/iPadOS software. If it is you'll need to remove/uninstall it.

The official Apple released OS upgrade/update version/s will not be present or be able to be installed whilst Apple OS Beta software installations are currently active and running.

In addition, if you have a iPadOS 15.7.1 or iPadOS 16.1 compatible iPad, that iPad year and model is, probably, waaaay too far behind in iOS/iPadOS upgrades/updates.

If you have access to a full computer, like a Mac or Windows PC, try either using the Finder on a Mac that has the newest macOS Catalina, or later macOS, installed OR with an older Mac with an older Mac OS, download and install the latest iTunes version ( or latest iTunes for Windows PC ), make sure the Mac or Windows PC is connected to the Internet, connect your iPad by the USB charge cable to the computer and let the iTunes application upgrade/update that iPad model, using the iTunes Software Update feature, to its current, maximum OS of iOS 12.5.6/iPadOS 15.7.1/iPadOS 16.1.1, depending on your year and model of iPad.

A 2013 iPad Air 1st gen, iPad Mini 2nd gen and 2014 iPad Mini 3 can ONLY be updated to iOS 12.5.6.

A 2014 iPad Air 2 and a 2015 iPad Mini 4 can ONLY be upgraded to iPadOS 15.7.1

Any other newer iPad model from late 2015 can be upgraded to the latest iPadOS 16.1.1.

At this late stage, use of a Mac or Windows PC is, now, unavoidable.

Make sure your iPad is, at least, charged to 50% or greater to attempt this.

Also, make sure your iPad has, at least, between 6-8 GBs of free internal data storage space for downloading and installing a major iOS/iPadOS upgrade.

Make sure your desktop/laptop computer has plenty of internal drive storage space, also.

Also, make sure to do a backup of your iPad's data, prior to upgrading/updating.

Backup to Apple iCloud and/or a full Mac or Windows PC using the same iTunes app OR, if a newer Mac running macOS Catalina, or later, making a backup using the macOS Finder app.

How to back up your iPhone, iPad, and iPod touch - Apple Support

If NO access to a Mac or Windows computer, you will have to seek help from a good friend or family member, with a full Mac or Windows PC, to help you out

OR

Search online to locate and call contact your nearest, “local” Apple Store location to try/attempt to make an appointment to get your Apple iPad upgraded/updated to its latest iPadOS 15 version.

OR, alternatively, use the “Get Support” link, at the upper right hand corner of every Apple Support Community Webpage to attempt to schedule an appointment with your nearest Apple Store location.

Apple Store employees will be glad to help/assist you.

Best of Luck to You!

Chances are your device cannot be updated further. Look under settings, general, about, find your model name then see how far it can be updated here

https://iosref.com/ios#ipad

My iPad 5 has no issues running iPadOS 16: