My second child was the same way! He ate every 10 minutes, and he was gaining more then enough weight, he was just hungry all the time, he never slept (he still never sleeps) and well the hole eating every 10 minutes ended at about 6 months, he still eats every 3 hours and he is suppose to be eating every 4-5 hours lol, but that just means you daughter is a good eater, it will get easier once you introduce solids and stuff.
As long as she is gaining weight, there's nothing wrong with how much she is eating. She's doing fine. At 5 weeks postpartum you're usually still engorged so it's normal if she doesn't fully empty your breast - you're body's still trying to figure out the right amount to supply.
However, if you are able to express, try keeping her on the first breast longer. My son would only eat from one breast each feeding, and I'd switch back and forth every time he ate. Sounds like you may need to start doing this.
As for her napping issues, it sounds as if she's having trouble getting comfortable. Have you tried laying down on your bed and nursing her until she falls asleep? I used to have to do this with my son or he wouldn't fall asleep.
Of course you don't want to do this when she gets older, but for now it's what she needs. Try laying down and cuddling with her during the first part of her nap time.
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