Actually, yes, the Nexus 5 does have native call blocking...or rather, automatically sending calls to Voicemail.
If you combine this feature with blocking the number within Google Voice, you can completely block a number.
If you're interested, this is what I did. ......... Enjoy.
Same basic idea but easier implementation:
On the phone:
- Create a contact named Banned (could be anything else too like blocked)...
- Add all numbers you want to block to it.
- Check the "All calls to voicemail" check box in top right menu of the contact.
On Google voice page:
- Goto Inbox (viz the home page once you login to google.com/voice)
- Pick and call from contact "Banned". Click "more" and "Block caller"
In future whenever you want to block any new number, just add them to the contact "Banned".
Simplest way to add: Goto your recent call list / call history, click the photo like square on left of the number you want to ban, click the top rectangle in the contact page (with a small + sign), which will open your contacts, now select "Banned" to add this number to it.
If you're impatient like me, you can goto Settings->Accounts->Google->Account you use for GoogleVoice and force the sync (full or only contacts), to push the updates you made on your phone's contact list to Google Voice immediately.