There are a number of views on these brothers and the specific meaning of this passage. We'll try to focus on just the brothers and not the passage, which has a long standing debate around whether it is even a parable or an actual account.
First, we shouldn't be focused on there being five brothers. There are six. The man in torment has five brothers, making a total of six brothers.
They are the brothers of Caiaphas.
One identification is that the man in torment is Caiaphus the High Priest. Josephus tells us that he had five brothers. So we are left the picture that innocent Lazarus is given unto Abraham's bosom, but the Pharisee, and his ilk, are given unto torment because they ignore the law. Considering Jesus attacked the Pharisee hypocrisy regularly, this explanation does make some sense.
They are the brothers of Judah.
Judah had five brothers from Leah, his mother, linking the five brothers reference to the Kingdom of Judah. Why the Kingdom of Judah would be singled out, I cannot say.
The number simply represents completeness.
Each culture has their own references to various things. In this case, five might have been a number that simply meant "whole." The parable of the ten virgins divides two groups into five and then they are judged corporately, not individually. This indicates in the same way that five represents the whole of that group. For the man in torment, "five brothers" represents his whole family, or even all those he loves. I personally find this the more reasonable answer.
The number is arbitrary.
Jesus is telling a story and needs to make a point, which is, that if you do not believe now while you have the law and the prophets, then even someone returning from the grave would not convince you. For this story to make sense, he needs the man in torment to have someone on the other side. Five sounds like a good round number and no one doubts that a man loves his brothers.
The author of this article deserves some credit for this post.