My daughter is a fabulous 14-1/2 year old babysitter who gets anywhere from $4-8/hr.
When she is asked, "how much do you charge?" She says, $4/hr. Honestly, she is thrilled with $4/hr. and I really hate to see people pay more. I had babies and they are the most important thing, huge responsibility, all that - I know - but seriously, you shouldn't have to go into debt to have a (much needed I'm sure) date with your spouse/partner. Adding a steep fee to a night out can put you well over $100 to grab a bite & see a movie! (Better be a good one!)
For a 10 year old, 5 hours, I would say $20 plus maybe a $5 "tip" (which they love), if they have done something a little extra = $25? And that actually sounds like plenty!
My daughter always cleans up, does any dishes left in the kitchen (hers or not) and does not talk on the phone unless it's to me (because I call to check often) And before all of the professionals get upset with me - let me clearly state that I am talking about teenagers here - this is not someone who has formal training or education for childcare - she's a teenager, and when it's appropriate, teenagers can be a great option. I have the utmost respect for anyone who makes a living working with children in any capacity and would almost always agree that you are underpaid!
She just needs a little spending money to hang out with her friends. (It helps me too!)