Q: Will the AirPods work with the iPod 5th Generation?

No. Not compatible.

AirPods requires an iCloud account, Mac Sierra, iOS 10, or WatchOS 3.

http://www.apple.com/airpods/

The 5th gen iPod Touch does support iOS 10, so it may support the AirPods. Apple make the fine print too small to read & don't list specific devices so I can't confirm, ask at a store if you want better advice.

No iPod Touch is supported under iOS 10 EXCEPT the newest iPod Touch 6th gen models.

Apple dumped every iPod Touch model for the upgrade to iOS 10.

Apple is thinning the iDevice "herd"!

iOS 10 LIST OF SUPPORTED DEVICES

Phone

• iPhone 7
• iPhone 7 Plus
• iPhone 6s
• iPhone 6s Plus
• iPhone 6
• iPhone 6 Plus
• iPhone SE
• iPhone 5s
• iPhone 5c
• iPhone 5
• 
  

iPad

• iPad Pro 12.9-inch
• iPad Pro 9.7-inch
• iPad Air 2
• iPad Air
• iPad 4th generation
• iPad mini 4
• iPad mini 3
• iPad mini 2
• 
  

iPod

• iPod touch 6th generation

No.

Apologies I was looking at the wrong model.

This

http://tidbits.com/article/16737

implies they will work by this statement

The W1’s technology is based on Bluetooth, so you can use W1 headphones with unsupported devices, but you will have to pair them just as you would any other Bluetooth device. It’s uncertain how the W1 pairing will interoperate with standard Bluetooth pairing.