Desktop extensions are not available yet, they are probably still "alpha", but might be beta by now.
Definitely not available in 10.5
You can still create something in HTML and use that to write back to the database, but you can't do that in Tableau. You would have to wait for a lot later in the year (I'm guessing) for that to be native functionality.
Perfect! Yes, that is the Developer Preview page for the Extensions API - it has everything you need to get started