I think the more experience and schooling you have that directly applies to Childcare the more you will be able to charge. Now maybe not $5+ more but I think $2-$5/day more is reasonable and justified.

I also left centre care due to issues I had with the way they operated and I started at $2-$5 more than the average hdc in my area. I've since increased it another $2 and I'm noticing more and more hdc's are charging my old rate and a handful are even charging more than me now so I think it benefited us all. Daycare fee's are one service that very very rarely increase but when a hdc increases it usually prompts others in the area to as well which I view as a good thing.

Don't overprice yourself though, stay within a reasonable amount and you will do fine! Good luck