Unless your DD has some sort of diagnosed medical condition that excludes dairy from her diet then you are not doing her any favors by not giving her any.
Proper Brain development depends on fat soluble vitamins that are contained in Red Meats, full fat Milk, Cheese, Yohgurt, Butter & Ice Cream.
Almost all your DDs carbs are coming from liquid & puree fruits. She is getting almost NO proper fibre, which is why she suffers almost constant constipation. She is not getting any dark green vegetables, spinach, beans, peas, cabbage, sprouts, broccoli, & other fibre rich veges carrots, peas, pumpkin, potato (not mashed) sweet potato, onions, celery, capsicum, mushrooms etc.
She is also getting very little in the way of good quality proteins, chicken, fish, eggs, etc.
A diet so high in fruit products will lead to candida albicans in the gut.
The MAXIMUM recommended daily intake of sugar in all forms ( Glucose, Fructose, Sucrose, Dextrose is less than 3 teaspoons for a child, your DD is ingesting about THIRTY teaspoons of sugar A DAY; 10 times the recommended amount.. Just because something says no Added sugar it does not mean that it does not contain sugar or a high amount of natural sugar.
Such a high sugar intake is setting her well on the road to childhood diabetes & adolescent obesity & a mouth full of rotten teeth.
The three things that are making the world over weight and killing us faster than ever are, Sugar, Vegetable oil (Especially Canola (Rapeseed) oil , excessive consumption of corn & Soy bean by products.
These products are touted because they are very high yield for a small area, cheap to produce and return a high profit. High Fructose Corn Syrup HFCS is basically poison, sugar is addictive.
Most margarine's are made from Canola oil, that stuff is toxic, if you saw how it was made you would never have it near your mouth again.
Most 5 year olds like canned tuna or salmon, that can be made into fish cakes, casseroles, bakes. My kids always ate it right out of the can they love tuna. They also ate Broccoli, peas, carrots, jacket potatoes, and most salad vegetables from a young age, eating off my plate as babies.
The only thing that children need to drink is water & the occasional glass of milk if they like it & maybe a very weak very small amount of juice a couple of days a week. A 200 ml glass of Black currant and apple juice contains the juice of about 4 apples and 300 gr of Currants, which is about the same amount of sugar as a 300 ml glass of cola, try eating all that fruit in one go.
Many kids like olives from a jar but remember that the are high in salt.
Start cutting down the amount of juice and fruit purees that you give her by at least half every day & start offering her the things you want her to eat, porridge for breakfast with a drizzle of honey & strawberries or Blueberries.
The ham sandwich is great but try to get more vegetables on it Tomato, grated carrot, mixed lettuce.
You have to keep offering better food choices and stop giving her the sugary rubbish, offer an apple cut up (NOT Peeled) with some cheese cubes as a snack. Many vegetables can be hidden in pasta sauces, zucchini, carrots, mushrooms, capsicums & in casseroles & the like, grate them, puree them, mince them, mash them.
New food Items need to be offered 5 or 6 times before a child gets used to the taste & texture; put the meal in front of them, give them 20 minutes to eat it and any uneaten portion goes in the fridge for later, DO NOT OFFER SWEET SUGARY ALTERNATIVES AND DON'T FIGHT ABOUT IT.
You Must be commited to changing her unhealthy eating habits, letting yourself feel good in the moment by giving in to her is not doing her any good or yourself any favors.
Consult a nutritionist & get some professional help if you feel you need it.