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.

Note that 5 Card Mission is the Meta Rule equivalent of the regular New Rule Goal Bonanza, and the Black Knight expansion for Monty Python also has a New Rule called It’s a Quest, which works in much the same way as Goal Bonanza (except it’s discard 3 Goals, and draw 4 cards to play).