I'm putting this under Health and not Nutrition because I think there must be an underlying health issue here. I'm not looking for suggestions on WHAT to feed her (unless it's to address a specific deficiency that might be causing the whole issue), but rather ideas on what might be going on.
My 5 year old weighs around 33-34 pounds. I don't know exactly how tall she is, but her height is normal, probably a bit on the shorter side but she's not stunted. But her weight is a problem!
She is hypotonic (low muscle tone) and received EI services for PT until she aged out. We didn't pursue further therapy because she has roughly caught up with her peers on global skills. She does swimming and gymnastics, and keeps up fine. Her energy level is fine, too - she doesn't tire extraordinarily quickly or anything. We have no diagnosis, just noticable (to us) hypotonia. She can run, jump, climb (just not as fast, high, or well as most 5 year olds).
Her father (DH) and I both were super skinny as children too, so we understand there may be something genetic going on. DH was hospitalized at one point for this, they didn't actually force feed him but they threatened it and were just really aggressive about getting him to eat. I was not hospitalized but it sounds like DH and I were very similar (maybe DH being a boy made them more concerned; girls are "allowed" to be skinny, you know?).
DD is a carb addict. I was a carb addict as a kid too. I grew up eating cereal (not Trix but Cheerios, Rice Krispies, that sort of thing - not that those are exactly great of course), bread, pasta and rice. DD likes the same stuff, plus fruit, and has the same sweet tooth I did. Except even when we feed her whatever she wants, she doesn't eat much at all. I try hard to encourage her to eat protein, but it's not easy. I can usually sneak some amount of fat into her food (for example, a fruit smoothie with a good chunk of coconut oil, or a nice spread of butter on her toast, or chick pea in a curry sauce with plenty of oil, etc.) but protein is harder.
I went grain-free a while ago just for the heck of it and was surprised to see that grains apparently were a problem for me. I never even suspected. My grain-free experiment was purely a shot in the dark. I suggested to DH that maybe we try DD on grain-free and see if her appetite increases and maybe her absorption too, but DH is scared to do it. And I see his point. We feel like she is barely eating at this point, and grains are almost the staple of her diet (along with dairy). I don't know if we can even afford to have, say, a few days adjustment when she doesn't eat anything, you know what I mean? On the other hand, if grains are a problem for her, I want to fix that. Dairy of course is another possibility, but I just don't know how to deal with adjusting her diet when it's so limited anyway.
I've heard zinc deficiency can lead to low appetite, so I am ordering Floradix Calcium-Magnesium supplement which has a decent amount of zinc. So I'll see if that helps her appetite any.
Honestly, DD's weight is probably normal for our genetics (my mother thinks I weighed the same, and it's a big family story about how my mother's sister supposedly weighed 35 pounds through first grade) but I want to do BETTER than just sigh and wave it off. If there is a mineral we're deficient in, I want to solve that. If we can't process grains, I want to eliminate those.
Oh, and the obvious answer is: see a doctor. Unless someone can recommend a very specific person that has very specific skills in this area, I'm not convinced. DD has been seen by 3 doctors (none recently) and they all had advice we thought was stupid. Like one instructed us to feed her ice cream every day, as much as she wanted. OK, yeah, we want her malnourished but diabetic. No thanks.