I think $5 is reasonable, but you should actually discuss it with her mom. I had a 13-year-old watch my boys at her home (our music pastor's daughter) and she has a 3-year-old sister there as well. I talked to her mom first about possibly having her babysit and then what her mom was comfortable with for her daughter earning. Parents have a say in employment at that age and might prefer that their kids not get overwhelmed with what is more money than they are used to. Her mom might also have some stipulations, such as when and where she could babysit.
I pay someone $7 right now for my two kids for a few hours at a time (usually someone in college or a friend) but it is cash each time. Once we have our third I will probably pay about $8. I round up, so when it is normally about 3 hours, maybe a hair more, I pay $25, so it amounts to a wee bit more but I like to keep things easy. I've babysat for anywhere from $5 to $10, depending on the family. I never set my own rate. The most kids I've watched were 4 or 5 for $8/hour. Some of them were school-age, though, so needed very little supervision. You could ask some moms in your area though because as several people have pointed out, babysitting rates vary by location, sometimes even within a city depending on where you live.