Fine, but to be actionable there would have to be damages. Taking such a claim to court would be expensive and without any strong likelihood of success.
And, as you note, the OP has not alleged that the rumors involve any allegations of criminal activity only that the person has said some bad things about the child (note that under CA law they could almost certainly never prosecute a 5-year-old for those offenses as a matter of law).
Now, IF such things were alleged, the 5 year old might be under investigation by the police, but not the person making the claim.
Given the experience I have had with people, I suspect that the OP may believe - as others do - that saying untruths about others is criminal. I have heard many people make such claims and call the police alleging a "crime" when people are talking about them or their family, so I would not be surprised if the OP thought that it could be. Heck, I've had people demand to arrest a neighbor for looking at them in a mean way or flipping them off! I have also heard officers tell people "We'll look into it," as a means to withdraw and get out of the situation without any intent of acting any further on it because it's not a crime.
This has become one of the most difficult sites on the internet to post to - I compose posts and submit them and they somehow disappear. I will try again.
What many people do not seem to understand about defamation "damages" is that there does not have to be a financial injury for damages to be awarded. A person defamed can be compensated for mental anguish, emotional distress, shunning, ridicule ... even when there has been no economic loss at all.
As a note, I am looking at the five-year-old child described in this thread as if the child has actually been defamed by the comments made by the adult (ie, false statements were made about the child and published to others). It would not be the child, in that case, who would be prosecuted for a crime because the child was only falsely accused of a crime (if that is what this is all about), but rather it would be the adult who could face prosecution (for example, for filing a false police report, bullying, harassment, whatever).
Admittedly, this is a stretch based only on what has not been related to us and based only on EV151's insistence that there is a problem for which a legal solution exists.
I agree that many people seem to THINK that there is a legal solution to all of life's problems and, of course, that is far from the truth. Sometimes barking dogs and pieces of plastic found in a fast-food hamburger and a trip/fall and bad-mouthing are just some of life's irritants that one must shrug off. It could be because of the number of attorneys in this country, or it could be because of the number of "free legal advice" sites that one finds on the internet that provide erroneous information, or it could be because of the media - but whatever the case, people often seem to threaten a lawsuit and police intervention when there is no clear justification for either.
However, on this site, and because we are provided with only one side of a situation and rarely provided enough facts to base a definitive answer on, I tend to suggest a personal review by an attorney in the poster's area. I would hate to deter someone from seeking legal assistance when there could be a legitimate cause of action for which relief can be granted. On the other hand, I understand that it is generally smartest to find a NON legal solution to a problem when such a solution exists.