My iPhone won’t pair with AppleTV. Error -5722

See here for a how-to: Pair your iOS device or Mac with your Apple TV - Apple Support

Do both devices use the same iCloud Apple ID account?

Is Bluetooth and Wi-Fi active on your iPhone?

Are both devices on the same home network?

1. You don’t need to pair for AirPlay, although a paired device skips manual authentication.
2. You don’t need to pair for the use of the software remote, although a paired device skips manual authentication.
3. You don’t need to pair in advance for Apple Fitness+. The Fitness app will ask for it when starting.