I am a strong believer that an allowance shouldn't be connected to regular household responsibilities. There are certain things that everyone must do to make our family run smoothly and just like your children, by daughter (5 y/o) has her own list of things she does to contribute. If I tell her my daughter that she going to be paid for those items, then what happens if she decides she would rather not do the chore (in "exchange" for not getting paid)? Do I just have to do those things myself or do I implement some other punishment to force her to do them?
I have a chart that lists the items my daughter is required to do daily (Hang up PJs, Make her bed, Clear her breakfast dishes, Feed & Water the dog, etc). I also have another list of weekly chores (Fold washclothes or napkins, Match socks, Dust, Empty Trash Cans, etc) and she is expected to select 1 of those to do each day. My "carrot", so to speak, is that she is only allowed to play when all of her responsibilities and chores are done. (I do try to phrase it in a positive way though. For example, "You can go play with a friend / read a book / color / etc as soon as you have finished your chore chart.") I don't want to link any of her chores to an allowance because she would frequently decide that she would rather play than get her $3 allowance at the end of the week.
I do believe that kids should get an allowance so they learn that their parents don't have an inexhaustible supply of money and also learn how to save up for things. I just don't think it should be linked to chores. I can understand the feeling that kids need to work for the money, but my parents did this method with me and I am (and always was) very responsible with money. It certainly didn't cause me to feel like I deserved money without having work for it, as I think some people might fear.
If you really can't stand to give your child money without linking it to work, another option might be to have a set of "extra" tasks (beyond normal responsibilities) that your child could do to earn the money. For example, shining the appliances, sweeping the kitchen, watering the flowers, etc.