how to update to version 16.5 on an IPhone SE

You cannot pick and choose an iOS version. What you get is Settings > General > Software update > [All options are available here]

If iOS updates are no longer being released for your device, it typically means that the device has reached its end of life in terms of software support from Apple. In such cases, there are a few options you can consider:

1. Although major iOS updates may no longer be available, Apple may continue to release security updates for older devices. Ensure that your device is running the latest available version of iOS for its generation to maintain the highest level of security.
2. As iOS versions advance, some newer apps may not be compatible with older iOS versions. You may need to rely on older versions of apps or find alternative apps that are compatible with your device's iOS version.
   1. Ask the App developer to release the app for lower iOS versions also. Netflix & Amazon has done it.
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3. If your device is no longer receiving software updates, it may be a good time to consider upgrading to a newer device that is supported by the latest iOS updates. Upgrading to a newer device will ensure that you continue to receive the latest features, security updates, and app compatibility. Selection of a mobile model/brand is driv… - Apple Community

Remember to regularly back up your data to avoid losing any important information during the transition to a new device.

It's worth noting that the availability of updates and options may vary depending on the specific device model and its hardware capabilities.

You must have a first generation iPhone SE, which cannot be updated to iOS 16. It is too old at this point.

A first generation SE cannot handle iOS 16.x. iOS 15.7.6 is as far as it can go.

If they are requiring you own an iPhone which can run the newest iOS version and they provide the phone, they'll most assuredly need to buy you a new iPhone.

Quite a testament to the longevity of Apple iPhone! Enjoy the new phone when you get it.