I just got my kitten at 5weeks old my aunt took them in cause the mom is an outside cat and stop feeding them she be trying to eat to fast when she eats and she vomited yesterday and twice today
It sounds like your kitten is eating her food way too quickly and it is coming back up. You can buy slow feed bowls or a lickmat to slow her down, or feed her small bits at a time so she can't eat it too quickly!
5 week old kittens aren't fully eating solid food yet so the food you are feeding may be upsetting the tummy. Are you feeding dry food or canned food? You may need to supplement canned food with some kitten milk replacer until the kitten is weaned in a few more weeks. Kittens have little tummies so small but frequent meals are best.
I suggest feeding smaller amounts every 2-3 hours, and use pate-style wet food made mushy with kitten formula. Make sure the kitten gets a meal before bedtime, and leave dry kitten chow and a saucer of formula available during the night.
As stated, at 5 weeks old, kittens’ tummies are tiny and because they are also growing so quickly, they need small amounts multiple times a day.
Can you ask your aunt to get the mother cat spayed? She will be pregnant again soon if not.