Keep in mind 5 is still young. Also if she has not been on this type of schedule, this is very new to her and she is having to adjust not only to the whole school thing, but a completely new life at home in the mornings.
You will still need to guide her a bit in the morning for a while... Just be as organized as possible the night before so the mornings are not so chaotic in the morning.
Here is what we did, for the first few weeks,I would get up before our daughter and get myself ready then, I woke up our daughter earlier than needed. I would give her "5 more minutes" to sleep and then I would turn on her light and watch her walk to the bathroom. I allowed her about 5 to 10 minutes to potty brush teeth and start getting dressed..
I actually said "you have 5 minutes to potty and brush your teeth".
I would then check, just peek, to see how far she was..
She then would put on her school clothes and shoes.
They were always decided on and laid out the night before.. Socks, hair bow, whatever was going to go with the outfit.
Then I would have her breakfast there for her. We had discussed the night before what she was going to have for breakfast the next day.. Our daughter never has been a breakfast eater, so instead of "morning negotiations", we figured it out at night.. Sometimes, it is not traditional "breakfast foods" and that is fine.. She might have a quesadilla, leftovers, a sandwich.. Or cereal and fruit, pancakes, scrambles eggs, PB&J..
Your infant does not need her clothes changed, just her diaper changed.. Maybe do this while your daughter is eating her breakfast.
The lunches should be made the night before. Your daughter can even help the night before by placing the non perishable items in the lunch bag and you place the perishables in the fridge. I also always kept a balance in the school cafeteria in case a lunch was forgotten, lost or we just did not have time to get it together. This way she knew she was always going to be able to eat lunch, no matter what happened in the mornings.
After the breakfast, is when I brushed our daughters hair. It was a lot of curly hair, so she needed my help.
IF we were ready early, I would let her watch a morning cartoon or video till it was time to leave.
FYI, Our kindergarten in Austin starts at 7:45 am I woke our daughter up at 6:30 am in the beginning to be in the car by 7:30.. But then we got into a groove, I woke her up at 6:45 and let her sleep till 6:55 at the latest.. (5 more minutes x2 she felt like this was a lot of extra sleep)