Yes, it is normal for a 5 month old not to tolerate food yet. Here's some information from Dr. Sears:
WHY WAIT? 6 REASONS
Gone are the days when pressured mothers stuffed globs of cereal into the tight mouths of reluctant six-week-olds. Nowadays parents feed their baby on the timetable that is developmentally and nutritionally correct -- as determined by their baby. Don't be in a rush to start solids. Here are some good reasons for waiting.
1. Baby's intestines need to mature. The intestines are the body's filtering system, screening out potentially harmful substances and letting in healthy nutrients. In the early months, this filtering system is immature. Between four and seven months a baby's intestinal lining goes through a developmental growth spurt called closure, meaning the intestinal lining becomes more selective about what to let through. To prevent potentially-allergenic foods from entering the bloodstream, the maturing intestines secrete IgA , a protein immunoglobulin that acts like a protective paint, coating the intestines and preventing the passage of harmful allergens. In the early months, infant IgA production is low (although there is lots of IgA in human milk), and it is easier for potentially-allergenic food molecules to enter the baby's system. Once food molecules are in the blood, the immune system may produce antibodies to that food, creating a food allergy . By six to seven months of age the intestines are more mature and able to filter out more of the offending allergens. This is why it's particularly important to delay solids if there is a family history of food allergy, and especially to delay the introduction of foods to which other family members are allergic.
2. Young babies have a tongue-thrust reflex . In the first four months the tongue thrust reflex protects the infant against choking. When any unusual substance is placed on the tongue, it automatically protrudes outward rather than back. Between four and six months this reflex gradually diminishes, giving the glob of cereal a fighting chance of making it from the tongue to the tummy. Not only is the mouth-end of baby's digestive tract not ready for early solids, neither is the lower end.
3. Baby's swallowing mechanism is immature. Another reason not to rush solids is that the tongue and the swallowing mechanisms may not yet be ready to work together. Give a spoonful of food to an infant less than four months, and she will move it around randomly in her mouth, pushing some of it back into the pharynx where it is swallowed, some of it into the large spaces between the cheeks and gums, and some forward between the lips and out onto her chin. Between four and six months of age, most infants develop the ability to move the food from the front of the mouth to the back instead of letting it wallow around in the mouth and get spit out. Prior to four months of age, a baby's swallowing mechanism is designed to work with sucking, but not with chewing.
4. Baby needs to be able to sit up. In the early months, babies associate feeding with cuddling. Feeding is an intimate interaction, and babies often associate the feeding ritual with falling asleep in arms or at the breast. The change from a soft, warm breast to a cold, hard spoon may not be welcomed with an open mouth. Feeding solid foods is a less intimate and more mechanical way of delivering food. It requires baby to sit up in a highchair – a skill which most babies develop between five and seven months. Holding a breastfed baby in the usual breastfeeding position may not be the best way to start introducing solids, as your baby expects to be breastfed and clicks into a "what's wrong with this picture?" mode of food rejection.
5. Young infants are not equipped to chew. Teeth seldom appear until six or seven months, giving further evidence that the young infant is designed to suck rather than to chew. In the pre-teething stage, between four and six months, babies tend to drool, and the drool that you are always wiping off baby's face is rich in enzymes, which will help digest the solid foods that are soon to come.
6. Older babies like to imitate caregivers. Around six months of age, babies like to imitate what they see. They see you spear a veggie and enjoy chewing it. They want to grab a fork and do likewise.
There is no real nutritional reason to have your baby eating solids this early anyway. So if she is responding that way, I would hold off for awhile. Hope that helps.
J.