This is a bit of a tricky question! It depends on what you consider a "mythological god" and how we define "named after". Here's a breakdown:

* Planets directly named after gods:

* Five: Mercury, Venus, Mars, Jupiter, and Saturn are all named after Roman deities. These names are derived from the ancient Greek gods they represent.

* Planets with names linked to gods:

* One: Uranus was named after the Greek god of the sky, but its discoverer, William Herschel, actually wanted to name it "Georgium Sidus" after King George III. This name didn't stick, and Uranus eventually won out.

* Planets named after mythological figures:

* None: While some planets are named after gods, none are named after mythical figures that aren't explicitly gods or goddesses.

Therefore, depending on the definition, the answer could be 5 or 6.

Let me know if you'd like to explore the history of planetary naming further!