Hey there Kyliesmama-
I think $2.00 a week for a 5 year old is an "age appropriate" allowance, however, if you feel like it should be upped, then that would be a choice only you can make.
Maybe try thinking of it this way, children LOVE to get money, and a dollar can seem like a hundred to little ones. An allowance of $2.00 a week isn't bad for a 5 year old, and at the same time, instead of hitting the dollar store constantly, try and help her to set a goal for something she would like to save for. Maybe take her to Walmart and find a toy that's maybe $10.00, right? Well, you tell her that if she can save for 5 weeks, she will have enough money to buy this particular toy. This way, you are also teaching her the value of working and saving your money for what you REALLY want instead of just spending the money you have because the money is there.
I don't mean that I think you let your daughter spend her money simply to spend it, because that's not at all what I'm trying to imply. It's just how my mom explained it to me when my kids started earning an allowance.
As they got older, I made a chart and hung it on the fridge. I set a certain monetary amount for different chores they could do (above and beyond their "set" weekly chores) to earn extra money, such as helping me dust would earn them another .25 cents, helping me vacuum would earn them another .25 cents, and so on. When they helped with an extra chore, we would check that item off on the chart and they knew they had done extra and would get the extra money with their allowance. They liked this system because it gave them extra money, and I liked it because it gave them incentive to help with extra things.
It sounds like your little girl is a great helper. Some kids want an allowance and don't actually want to earn it, ya know? You are already teaching her a valuable lesson and this is a good thing.