Hello, I'm Dr. Deb. Thanks for requesting me.
I'm so sorry to hear about the kittens that you've lost; it must be really hard to see Abby starting to decline as well.
In situations such as this, I always worry that there is some birth defect which is causing what's known as Fading Kitten Syndrome. Other possible causes include a bacterial infection originating from the gastrointestinal system, respiratory or urinary system or a virus such as feline coronavirus, feline panleukopenia virus, or feline leukemia virus.
If a bacterial infection, then many of these kittens will respond to antibiotics but viral conditions in kittens this age don't usually have such a positive outcome I'm sorry to say.
I don't want to sound as if there's nothing that you can do for Abby but, unfortunately, you are going to be limited since there are so few over the counter options for you to try.
First, I'd want to take her temperature to see if its elevated. Normal is between 100 and 102.5; if it's high, we still won't know if she has a viral or bacterial infection as the cause but I'd want to start her on antibiotics in hopes that it's the latter.
Low blood sugar can be seen in some kittens so I'd rub pancake syrup or honey on her gums every several hours to see if this will help to stabilize her.
At five weeks of age, most kittens will already be weaned from their moms and starting to eat kitten food
on their own. You might offer her canned food to see if she has any interest rather than continuing to try and bottle feed her. However, if she refuses, another method for nursing kittens (and puppies) is with a cosmetic sponge. The following link provides a video which demonstrates the process with a puppy but it would be the same for a kitten.
I'm truly sorry that I can't provide a more positive response for you but if she continues to decline, then a vet visit may be prudent.
Kittens this age don't have a lot of reserves as you no doubt know and can deteriorate quite rapidly.