Try reading the FAQ:

  Why don't I see down arrows?

  There are no down arrows on stories. They appear on comments
  after users reach a certain karma threshold, but never on
  direct replies.

Since your account was created 5 minutes ago, you lack the karma to downvote.

Downvoting is enabled once you hit 500 karma, a policy presumably meant to ensure that those most likely to contribute to a quality discussion are also the most likely to have good judgement in downvoting less quality discussion.

There is a downvote button after you have gotten some karma.

See: http://i.imgur.com/dqItM9R.png

Downvote buttons become visible when you have sufficient karma to vote something down.

Not everyone lacks downvote buttons. I have them. I don't know how you get them, but I assume it's related to account age and/or karma.