Right now it requires a 3000 reputation to cast a re-open vote.
I am not as concerned about closing votes as I think it should be a rare occurrence and we should lean towards helping people make their questions and answers better.
However, the fact that it only takes five people to close votes out of thousands of users, and only the rare few that have attained over 3000 reputation, does seem kind of unfair.
I also can see though how you wouldn't want people that are relatively new closing questions as they may not have enough experience yet.
But to re-open should be different and here's why.
If someone is a casual user or somebody who enjoys reading more than writing, their voice is completely squashed by this system. Someone might ask a good question, five people out of a small pool of the 3000 plus crowd vote to close it for whatever reason (and it might not be a good reason). And remember that pool is even smaller than you think because most people only read posts that they're interested in (I read Star Trek, and some Harry Potter, others may only look at Star Wars or a favorite author, etc.). And there's hundreds maybe even thousands of users that don't have 3000+ who would like to read and/or answer those questions, and they can't do anything about it.
I think we should lower the re-open reputations significantly. We should lower it to 500 or maybe 750 reputation. At that number the person is a real member of the community, has been participating, and should have their voice heard.
What is the process for doing something like this?