iOS 10/11 iPod Touch 5th Generation
The iPod Touch 5th gen is ineligible and excluded from upgrading to iOS 10 AND iOS 11.
The, now, 5 year old hardware architectures and a less powerful, clocked down 1.0 Ghz CPU that Apple has deemed insufficiently powerful enough to even run the basic, barebones features of iOS 10 OR iOS 11!
In addition, the 5th gen iPod Touch has the same paltry 512 MBs of RAM as the iPad 2 and 1st gen iPad Mini.
Why would you want to upgrade, anyways?
The 5th gen iPod Touch models had only been getting the most basic of iOS 9 features!
The 5th gen iPod Touch got NONE of the new and cool features of iOS 9.
Plus, with the 5 year old technology inside of the 5th gen iPod Touch, iOS 10 OR 11 would have severely slowed the device down with even the installed base features of iOS 10 or 11.
FYI,
Just because your iPod Touch 5th gen is no longer able to upgrade to the latest iOS doesn't mean your iPod Touch 5 is suddenly useless.
Your iPod Touch 5 will work as it always has and the apps you have installed on it will continue to update and receive some level of app updates relevent to your current iOS.
You have had four years of iOS upgrades and updates.
Your iPod Touch 5th gen will still do everything it does now and you will, get, at least, another full year, perhaps two, if you decide you want to wait longer to get a new or newer iPad model.
Your iPod Touch 5 is NOT, suddenly, becoming obsolete or useless.
So, your options are really keep using your iPod Touch 5 or purchase a the “new” 6th generation iPod Touch if you feel you need or want to.
Your current iPod Touch 5 will still work and continue to receive app updates for some time, when, with the recent introduction of iOS 11, ALL support for older 32 bit iDevices and any iOS 32 bit apps will come to a final end.
Your iPod Touch 5 will still work and function as it always has, but will no longer receive any more app updates some time in the foreseeable future.
The final app updates your 5th gen iPod Touch will end up receiving will be their last!
Your iPod Touch 5th gen should STILL be receiving app some updates, currently, but look for this to end sometime soon.
Currently, your ONLY option is to upgrade your 5th gen iPod Touch to the current 6th gen iPod Touch models.
Good Luck to You!