Welcome, Dan.
You'll need to remove that top layer of flooring, which in your photo appears to be what would usually be called strip wood flooring rather than "planks" as you suggest.
Then you would need a minimum of nominal 1/2" plywood over the 5/4 board subfloor before your tile substrate.
The minimum nominal 5/8ths" plywood requirement you see for most CBU manufacturers presumes that material as a single layer subfloor, which I would not recommend tiling over on a bet.
My opinion; worth price charged.