How do I update my iPod 5 to ios10

An iPod Touch 5th generation cannot be upgraded/updated beyond iOS 9.3.5.

It’s a 6-year old iDevice with internal hardware that is too old and underpowered.

If you need older versions of apps for that device, tap and read over my possible three solutions to get initial, older versions of apps for the model iPod Touch.

Downloading Older iOS 9.3.5 Versions of Apps ONLY Available Now for iOS 10 or Later

You will be unable to update that device to iOS 10 because it is not supported. Check out this link for a list of supported devices: iPhones and iPads that will -- and won't -- work with iOS 10 - CNET