Q: If I am executing a 5 Card Mission, and I have a card which would make me win, and another which would negate that, can I play the winning card, and stop there, or do I have to play all the cards?

A: As long as the negating card is not a Creeper (see this question) you can play the card which would make you win, and the game would end (assuming it’s not stopped by a Surprise, of course). You do not have to play all of the 5 Card Mission cards and THEN assess your win status.