5. It's a bird. It's a plane. No, it's a pterodactyl, that is neither a bird nor a plane.
This is not exactly a question of punctuation, though punctuation is an issue here. It's a question of essential or non-essential elements. Other terms you might have heard are restrictive and non-restrictive.
In American English, the word that is used in essential clauses or phrases. The phrase that follows that is essential to the meaning of the sentence. The word which is used in non-essential clauses or phrases.
A phrase that begins with which is not essential to the meaning. For example, the sentence above makes sense if you end it after the word pterodactyl. If you want to include the additional information, you should write No, it's a pterodactyl, which is neither a bird nor a plane.
Remember, use a comma before which but not before that.
This old that/which issue is a bit tricky. Try another.