Broken screen on iPod touch 5th generation, what is the replacement or repair cost?

Apple will exchange your iPod for a refurbished one for &99 for 16 GB 5G and $149 for the other 5Gs. They do not fix yours.

Apple - iPod Repair price

You can do it at an Apple store by making an appointment:

Apple Retail Store - Genius Bar

or send it in to Apple. See:

Service Answer Center - iPod

A third-party place like the following maybe less. Google for more.

iPhone Repair, Service & Parts: iPod Touch, iPad, MacBook Pro Screens

Replace the screen yourself if you are up to it

iPod Touch Repair – iFixit

You can actually search over Amazon and find a replacement Digitizer and then go to fixit.com to get the instructions on how to fix it if your confident on fixing it yourself.. If your not confident, you can take it to a certified Apple Technician and see what the pricing options there or find a service in town that will also do it.

To repair it... Costs could range around $35 to $59 total not including shipping for the items... ifixit.com will tell you all the tools that you need and everything..

Hope I was able to help! Any more questions let me know.