Is this the right part for this model?

I was given a Kindle Fire, functional but the glass is cracked. The person who gave it to me doesn't know what model it is, and I know next to nothing about Kindles. According to Settings->Device Model this is a "Fire (5th Generation)" but according to this web site -- https://www.epubor.com/how-to-tell-kindl... -- this is a "Fire HD 10 (5th Generation)" based on the fact that the serial number starts with GOOO (or G000).

Is a "Fire (5th Generation)" the same as a "Fire HD 10 (5th Generation)"?

Assuming "yes" to that, would this glass -- https://www.ebay.com/itm/122719924763 -- be the correct replacement for it?