During the game, if I lay a five and then a king, I know that's 15 and thus scored "fifteen-two." Can I then lay a 10 and add it too my original five to make a new 15 and score two more points?



During the play, you can only score 'fifteen-two' once - when you make the total 15. If you make the total 31, you can score another two points. Although you can count runs (eg 4-5-6) during the play, combinations of cards making 15 don't count for anything, unless they make the total 15.

They do count during the scoring phase of course. I hope this helps!