$3-5 per hour was the rate I was paid to babysit as a teenager in the 70's.
First of all, you should have a contract, specifying your responsibilities,pay, hours, vacation and other paid time off,etc. You are allowed to say no to say no to demands that don't work for you.
For a five month old, everything is fun! Read,read,read to him/her, take them for walks, describing everything you see, sing (they don't care if you have a great voice), play music,give them lots of safe toys to reach for, grab, and chew on,plenty of... more
You should be paid overtime for any hours in excess of 40 per week. Sixty hours? That's 20 hours overtime. Why even have children if someone else is caring for them 60 hours a week? SMH...