When should the woman start initiating dates?

I've had 5 dates with a guy, all initiated by him. Basically, he asks me when will we be able to meet and I normally come up with an idea on what to do. However, when do you think it's appropriate for met to ask him out? I don't want to come over as needy or claiming. I also dont want him to think he is the only one putting effort.
When should the woman start initiating dates?
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