Age 5 is a common age when parents start thinking about issuing an allowance to children. The goal with an allowance is to teach children about personal finance and delayed gratification. Children who practice delayed gratification tend to be more successful in life. Thankfully, this is a skill that can be acquired with practice. You may choose to tie the allowance to chores, or not. There are two schools of thought on the topic, which you can read about here. Personally, I thought everyone tied the allowance to chores but after researching this article, I am considering the alternative. There are certain things that children need to learn to do for personal hygiene or to be considerate while living with others. If they don't do these things, taking away an allowance may not be enough to motivate them, leaving the chores undone. Rather, you can take away things like attending a birthday party or the car keys if they don't do these basic requirements of being a family member. An allowance can be seen more as a way to allow children to learn from their money choices and make mistakes now, versus when they are 18 or older.
Experts vary on the amount of allowance to give, but a formula based on age per week (say 50 cents or $1 per age) is simple, and easy to follow, even as they get older. Some parents issue allowance monthly versus weekly, or round to the nearest dollar so they don't have to worry about the change. Choose a system that you can realistically afford and maintain over the long-term.
We use the Jar System in our household. It consists of 3 jars: Charity, Savings, and Spending. A child splits her allowance into each jar by the following percentages: 10% to charity, 40% to savings and 50% to spending.
This can go towards a charity that interests the child, such as an animal shelter or place of worship. My daughter used to attend a school that allowed a different charity to solicit money from the children virtually every week. They would tell the children that if they donated $5 or $10, they would get some knick-knack. My daughter got very frustrated with me for not giving her the money, but I told her we already donate all we can afford to the charities we most care about and have researched. She started giving money from her charity jar. The first time, she emptied her jar completely on one charity. The next week, another charity came that she would have preferred to give to, but she had no money left. She is learning to be more thoughtful about who she is giving to and why, and she tries not to completely empty her charity jar on any one cause.
This can go to any immediate wants. Examples in our household include gum or mints, which I don't typically purchase for the children. It is so nice to be in a grocery store or Target and just say "You don't need that, so you can buy that with your money if you want." It prevents anyone from getting emotional, and clarifies the way things work: We, the parents, will provide your needs and a small allowance, and you get to choose how to spend that allowance. We need to be in control of our budget, just like you.
You can put this money in a bank account for them or add 2 cents for every dollar they have in their jar at the end of the month. This will teach them about "compound interest", where they earn money on the savings, not just what was put into the jar originally. You can let them dip into this savings at their discretion or require they save it for long-term expenses like college or a car.
Interested in books for children about personal finance? I read all of these books and can personally recommend them.