2 player pegging during the play

Setup: During 2 player play, my opponent played extra cards after a go to get to 31 and took his points, leaving him with one card. I still had 3 cards, all 5s. I play a 5, he also plays a 5, taking his 2 points for the pair. That leaves him with no cards. I play one of my 5s, making 15. I take the 6 for a three of a kind and 2 for the 15 score. Yes? Another question: My last card is also a 5 which would make the count 20. Do I get the 12 points for the 4 cards being all 5s? My view is the cards are still live until reaching 31 even though he has no cards. (He rage quit so it's a moot point but I wish to know if I was right.)