Turning in cards when you have five or six cards
You can only get one card per turn so you would never move from 4 to six in one turn.


Not true. The rules of Risk state that you get the cards held by an opponent if you eliminate them from the game. There is the additional condition: When you get enough cards from an opponent that brings you to six or more cards you must immediately turn in sets until you have four or fewer cards left over. (You must stop if you have four or three cards and have another set to turn in.) 

But consider the case where you start your turn with four cards, then eliminate someone with one card. You gain the card, giving you five cards. At the end of the tern, you've captured new territory so you draw another card. This gives you six cards at the start of your next turn!

So therefore it's possible to have up to six cards at the start of your turn, but no more than that. The rules explicitly state that if you have five or six cards, you must turn in a set. Having five cards and waiting for the sixth isn't playing by the rules.