Deadset against this.
When people vote to close questions, the question is merely closed to new answers. Existing answers can still be voted on, commented on and edited. It takes moderator intervention to prevent those things or to delete the question.
Even if the question is offensive or spam 5 users can't delete the question. 6 can flag it resulting in 100 rep loss. If it gets sufficiently downvoted (-10 or below?) I think an automatic process may delete it. It can also be flagged for moderator attention.
But you want to give delete power to 5 users to answers that they deem are duplicates? That is more delete power with a lower barrier to entry for something that isn't even spam, abuse or offensive? No way.
Often duplicates end up there because two (or more) people post the same answer within seconds of each other. Should one be penalized entirely for being 1 second slower than someone else? They already suffer enough of a penalty in that the first answer will generally attract more upvotes although some people will vote up both/all duplicate answers if they're all posted reasonably closely together (in my experience).
The problem is here is that users are disincentivized from cleaning up and deleting their own content. By that I mean that if your content gets upvoted and you tehn delete it you'll lose that reputation on the next recalc. We are generally talking a small number but the point remains there is no incentive and a minor disincentive to delete duplicate content.
I've previously proposed that deleted content should get the HIGHER of 0 and the reputation the post got on a recalc for exactly this reason.