My iPad keeps failin installing an update- An error occurred installing iPadOS 15.5

Assuming your iPad model supports iPadOS 15 or later, as per this compatibility list:

and assuming you're trying to update your device wirelessly, and bearing in mind that to perform such a procedure you need to connect your device to a reliable and fast Wifi Network with Internet access (no cellular data, unless you use a 5G network, no personal hotspot on your device, no VPN connections are admitted, no Low Power Mode enabled, and I suggest that you keep the device plugged into power during the whole update process), read this support article:--> If your iPhone, iPad or iPod touch won’t update

Keep in mind that, depending on the available storage on your device and/or on your wifi network speed, it might take 30-60 minutes to complete the entire update process.

If the issue persists or if the iOS version currently running on your device is very old, try to update it via computer (if you don't have a computer borrow one from your friends/neighbors, or ask for help at an Apple Store or Authorized Service Provider), then learn how to update your device manually if you're using a Mac with macOS Catalina or later, or if you're using a Mac with macOS Mojave or earlier or a Windows PC.

If you still get no help, contact Apple Support directly, using this link:--> Get Support

Regards

Giulio

We have been having a similar problem with one of the iPads in the house. Wouldn't update on the IPad to IOD 15, continually failing giving and 40xx (can't remember the exact number) error code.

Tried this evening to update via my McBook, and got the same issue (after about 30 min of not appearing to do anything.), then I tried again (because) and it worked.

So basically keep trying!