Does this mean you teach 5 cards from EVERY category 3 times a day?
Not from every category, but 3 categories that you have chosen for the day. This is a general guideline, and can be modified according to your child's interest.
Example: A set of cards from the category "animals". Do you teach the same 5 words from "animals" 3 times in one day, then the same exact cards the next day, 3 times in that day too, or do you use 5 different cards?
According the the Doman method (if you choose to follow it), you would retire a word and replace it with a new word for every category, every day. However, not everyone does their lessons according to the Doman method. I, for example, play whole new categories every day. So if I play animals, shapes, and colors today, I would play dinosaurs, body parts, and birds tomorrow. I think this keeps things much more interesting for a child.
Also, if you have 4 categories, and you teach 5 cards from each category 3 times each day, isnt that a too many lessons? That would be 15 lessons a day! Is that what the instructions are, or am I just confused?
No, that would be 3 lessons a day. You show all the categories in one session, wait a while, and then show them again, and again later. So your child actually has 3 sessions of 20 cards (if you are showing 4 categories with 5 cards each) 3 times a day. If you flash them fast, a 3 or 4 category session will only last a couple of minutes.
I hope I cleared things up, if not, let me know.