The laws can vary from state to state on what type of car seat a 5 year old should be riding in.
In some states a 5 year old can move out of a harnessed car seat and move up to a booster seat.
If the 5 year old can fit in the seat belt properly with a booster seat then the 5 year old can sit in a booster seat instead of the harness car seat.
My 5 year old would not want to ride in a child car seat with the harness straps because he said those were for babies but he will sit in a booster seat which he is required too by law.
I wish he would sit in the harnessed car seat because it's safer and he still fit in it but as long as he rides in the booster seat then I'm okay with that.
Usually once a child reaches 4 years old they can sometimes ride in a booster seat instead of a regular car seat but it depends on their weight, height and the laws in your state.