iPhone 12 Max Pro won’t download the new iOS 15.5

To update over the air from the phone all of these requirements must be met:

• You need at least 6 GB of free storage
• You must be connected to a Wi-Fi network (and not a personal hotspot) unless it is an iPhone 12 or 13 series with an active 5G network connection
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN, and it may be necessary to delete any VPN apps and VPN profiles
• The phone cannot be in Airplane mode
• You cannot still have a beta version installed on the phone<—This is a good possibility
• You cannot have a previous version that was downloaded, but not installed - go to Settings/General/iPhone Storage to look; if you find an iOS installer, delete it

If you can't meet all of them you can still update using your computer.