This idea should not be implemented.
Closing is done by community
One thing should be made clear, although it is 5 specific users who vote to close, those 5 specific users are acting as a proxy for the entire community. If any question had not been closed by those 5 individuals, it would have been closed by five other individuals.*
* It would be irrational to believe that the only 5 users who want to close your question all coincidentally happened to see it, unless they were ganging up maliciously, in which case, contact them would not change their minds.
So it isn't that you necessarily need to convince those 5 users to reconsider, it is that you need to convince any five users to reconsider. For that reason, you'll have a much better success rate by taking your cause to Meta and pleading your case here. At Meta, you'll find users who are engaged and interesting, willing to show you where you went wrong if that is appropriate.
Your Feature Request: Notify the individuals
Most users on StackOverflow are closing and then moving on. The analogy is of picking up litter and putting it in the nearest bin. You've done something good.
Once we start spamming those users with notifications, it is a disincentive to continue closing questions. My vote to close is not an indication that I want to engage and discuss with the OP, it is nearly the opposite, in fact. I have just explicitly shown my disinterest in engaging.
I have already written about this here: Notify On Edit Of Closed Question
Basically it comes down to punishment/reward. When I close a question, the reward is a cleaner more consistent site, the punishment being the possibility of someone disliking me for it. [...]
Once this solution is implemented, [...] I could be notified [for] every question I've ever voted to close on. [This will cause] sending out many many notifications to people who don't necessarily care. So you've added "punishment" (that is, undesired results) to the close action.
I do have an alternative that does not involve notification or spam of any kind
"Edited after close" view in 10k tools
Read there for more details.