Ouch! Tough scenario.
You're right that it's indicative of low self-esteem, or at least a desire for asserting control and power. I know that some schools have done very well with bullies by simply giving them responsibility, if they are in charge of taking care of the school pet or a similar small responsibility, their motives are directed towards the collective and they become a much more productive member, and grades have even improved.
I strongly recommend a thorough talk with the child at every instance they show this behavior, asking them:
- Why are you doing this?
- Do YOU think it's wrong that "whoever it was" did that?
- Are you mad at "whoever it was" ?
- Do you know this hurts people? Do you want to hurt them?
It's very important to take a moment to really listen to what the child has to say about it. Part of the "snitch" appeal is shaming the other person, so if you increase self-awareness and make the child realize that being malicious in the form of snitching is considered bad too, you may get through to them. That in combination with giving them some more responsibility will hopefully steer them clear of this bad habit!
EDIT: a child who is 5-7 really doesnt think about their actions that much, most dont have much self-reflection because they are just learning to be social. Asking them self-reflecting questions asks them to form opinions about themselves in a way they might not have otherwise, which can improve their behaviour if guided positively.