Why does ios 16.4 for me takes 5 hours to install

The time it takes to install an update is determined almost entirely by your internet connection speed. The time to update has 3 primary components: Download time, verification time, and installation time. Of these the first is by far the largest contributor. The other two typically take about 15 minutes. On my 1 GB internet connection the whole update takes about 20 minutes. There are other factors that can slow it down. If any of the following are not met or are only intermittently met, for example:

• You need at least 10 GB of free storage for iOS 16 or 6 GB for iOS 15 or lower; more is better
• You must be connected to a Wi-Fi network (and not a personal hotspot) unless it is an iPhone that supports cellular 5G (12, 13, 14 or SE 3rd edition) and has a 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 and must have a cellular data connection
• You cannot still have a beta version installed on the phone
• 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.