To let a five year old do whatever she wants

First of all, there is a saying in behavior psychology that states,

The behavior is controlled by its consequences

Then, if a child of 5 years is doing something wrong is because she/he has been rewarded with words when she/he does something non-desirable.

A child must be praised often for anything he/she does right, and even when he acts on something not specially interesting or desired. A child has plenty of time to do a lot of things that deserved praise, and a lot of things, or acts that are indifferent. We must rewards with praises and comments those types of behavior.

But what happens when a child does something objectionable, or non desired?

According to the behavior science, we must ignore what he had done. We must look sort of not being aware of what he/she has done. Why? The child is expecting praises and attentions from parents and relatives around. He/she is very eager for praises and is constantly doing something. Sometimes he/she does something you do no desire, or that is objectionable. Why he/she does it? The child is expecting his mummy or daddy to say something. But if his daddy or mummy ignore what the child has done, he is learning that this sort of behavior is not productive. Her father or mother is not rewarding this sort of behavior.

I would put a few examples. My daughter in law, and sometimes my son, sometimes is insisting for his kid of 20 months to eat more. I advised them not to behave this way, for they are creating a problem for the near future. You put the plate with food on the table, and if the girl is hungry she would devour the food in a moment. If she is not hungry she would eat very little or nothing. We must shut up and do not comment on her attitude. After 10 minutes if she is not eating, we must retire the plate off the table. We can put the plate in the fridge for not wasting the food. There is nothing more. We cannot argue with a child for any reason. If she must put on her shoes, you put on her shoes. But do not argue, or comment, because she does not put on her shoes. If she has said, I do not want to put my shoes, you cannot start arguing with the child. This happened once, when my daughter was five or six years old. Her mother started to insist that she should wear her shoes. She opposed the idea and said not. She started to argue for a while, and her mother was a bit upset with the argument. The mama told me about the problem.
“Go and talk with daddy.” she said.
I asked her,
“What is the problem?”
“I do not want to put my shoes”.
“It is OK. Never mind. You can go barefoot.”
She was so happy that I understood her. Se was learning to argue with her mum. The pleasure of an argument it that the other side replies to what you are saying.

(Here I confess I am eagerly awaiting someone is going to dispute what I am saying here.)

It was summer and my daughter was so happy barefoot. The mama had decided to visit some relatives living near the harbor. She thought it was no decent to go with a child barefoot. We were not so poor. I do not minded at all. Nevertheless, I told the mum put the shoes of the girl in the bag for later.
“OK, we can go.”
I turned on the key and we were about to leave. My daughter was very happy. But as soon as she began to step over a path of sharp volcanic tephra, she was feeling the sharp needles the black tephra under her feet. As she felt the mortification of walking over the tephra, she asked for her shoes.
“Mama, I want to wear my shoes.”
I would had been able to bring her walking barefoot on the sidewalk all the way to the harbor. The place was 20 Km away, and most of the way had to be done on a car. But it does not make any sense to start arguing with a kid for such a silly thing. The reason is the parents voice is rewarding, it is pleasant to hear, so it is not a good idea to start arguing with your children. A child can get hooked if arguing often with the parents. It is not the fault of the kid, it is the fault of the parents.

If we often start an argument with children it would become an undesirable habit, and the problem will keep growing with the child. The most a child grows, the more will grow the problem.

Then, if a child is rewarded for a swift obedience always or almost, she would be a very obedient child. But we must be alert to be ready to reward the child after he executes the order or a petition.

Then, what happens when the kid does not obey instantly?

We should not repeat to order, or the petition.

On the other hand, it is a lot better to ask the child something with polite manners. But if the child ignores the petition, we must ignore the fact as well. We must behave as if nothing had occurred at all. We must not repeat the petition or the order. We must feigned that nothing had occurred. But we must keep in mind, that we were being stingy with our praises when the kid had obeyed more or less at the moment. If we forget to praise a child when he obeys, the idea of obeying looses all its appeal.
And otherwise, if we rebuke the child for not obeying, the child is learning that to ignore a petition or an order is a lot of fun. It can start easily an argument.

Then, it seems like the parents that are modulating the undesired behavior of its children.

It is parents that deserve a spanking for doing things wrong.