I'm honestly surprised at how many people think he should take the draw. I can't even imagine offering a draw in blitz chess. It just seems to me to be contrary to the spirit of the game.
I play blitz chess differently than I play regular chess. For example, I almost always will trade a knight for a bishop in blitz chess, knowing that a bishop in the end game can lead to a quicker checkmate. A knight game is more likely to result in a run down clock. I throw people into useless checks not because it will lead to a long term gain, but because it's a two second move for me that might require my opponent to spend 10 seconds, and put him in a position where he's in unfamiliar territory, which takes more time. Sometimes I sacrifice pawns to gain time on the clock.
In a "real" game, I would never do it, but in a blitz game, absolutely.
My own view is that all Blitz games should be played on an increment basis.
The only reason that 5/0 exists is because in the old days all clocks were mechanical and could not handle increments, Digital clocks have removed this problem.
So long as the guy is prepared to be big about it when he gets shafted like that I dont have a problem.