I'm posting this not as a question but a resolution to a problem that I experienced. I also wanted to mention that Verizon support was not able to help me properly since the Nexus 5X is not a phone supported by Verizon even though services function perfectly.
Problem: After listening and clearing out 6 voice mails, the voice mail notification on my Nexus 5X just wont go away and displayed that I have 6 voice mails. I restarted the phone and nothing worked. Left a voice mail to myself and cleared it out and that did not work. Called Verizon for support and they couldnt assist either.
Solution I discovered: Go to your settings -- > Apps -- > Click the more icon at the very top right corner (the 3 dots) -- > select "Show System" -- > find and select "Phone Services" -- > click "Force Stop".
This will stop your Android phone services and clear out the voice mail icon, clicking your phone app icon (the icon to dial a number) will restore/start your Phone Services back and the Voice Mail icon has been successfully reset.
I hope Verizon uses this method for user support in the near future.