Depend on the situation.
If 2-3 players are banned and the rest think of Drawing for fair play, you are obligated to do so as well.
If it is a fair play, then take a look on situation first.
If you are leading ahead by large margin, give couple of turns before Drawing (if you can't get Solo).
If you are not the leaders, and the three biggest players have agreed to Draw, then better Draw before everyone thinks to get rid of you before Drawing.

No. With six players, there is almost always lots of interesting play left. A six-way draw is only very marginally better than a seven-way (i.e. no result at all). I find it very unlikely that 5 good players will all vote draw, unless you're close to winning. And then the draw vote is rather pointless.

Now, if you are actually losing, totally accept that draw. But let's consider the more interesting scenario, where you're on the winning side and everyone votes for the draw out of fear for you. Your job now is to convince the other major powers that you're not a solo threat and plan to eliminate the weaker players. What if they refuse and insist on attacking you? Well, that means you've made a diplomatic mistake, and you have to negotiate again. In the worst case, you'll lose a few centers and then someone else will take the lead (and remove their draw vote).

There is one exception: in gunboats, strong players will often use the draw vote to communicate peaceful intentions.

You've neglected to specify the map - is that 5 from 17? or 5 from 7?
The critical question is (IMHO): gunboat, or not? If youre in a game with press, you should expect to be persuaded to draw, not obliged.

Except in the case of lots of banned players, I don't see that you're ever honour-bound to draw. If you're winning....WIN!

@Basvanoph - a 7-way draw is one of the hardest diplomatic victories to achieve, i mean you might be able to get one ally or two to draw, but getting them to include everyone? Definitely one of the best results you can hope to achieve...

but back to the thread question - it depends on the game. If you agree to sit down with 6 others and play a game of dip, and something goes wrong which means you can't play, then you should cancel and start again or pause and play later. If you have reached a stalemate and there is no further progress then you should draw.

Those are the basic situations and important considerations.

If people are bored of the game and don't want to play anymore, then you are free to decide for yourself how to respond.

basvanopheusden has supplied the correct answer. Ideally, you will seek to win the game. If other players are seeking or attempting to force a draw beforehand, they are probably noobs. Only noobs will seek to draw a game with more than three remaining players.

A five or six way draw if fairly embarrassing.

"Only noobs will seek to draw a game with more than three remaining players."

Really, Al? gameID=122438