Actually, they got put in both a public and private human zoo, depending on the time in their lives. The first quintuplets ever to be born were in Canada in the 1930s. They were promptly taken away from their parents and put in a viewing center for the state. When they got back to their parents things didn't get much better.
Even today, during the age of fertility treatments, quintuplets are unusual. In 1934, they were unheard of by most people, and only rarely discussed among doctors. No previous sets of quintuplets survived infancy, and so when Elzire Dionne in Callander, Canada gave birth to five healthy girls, it became international news. Knowing that the family would need support, people sent money, donations, and advice. Perhaps it would have been better if they hadn't. Many people took notice of the money coming in to the Dionne home, a poor homestead outside of town. When the quints were about four months old, the government stepped in, stating that they couldn't be properly cared for by the Dionnes removing them to a newly-built house just across the street from the hospital where they were born.
There the quints were put in the care of staff, and were given constant tests, from x-rays to psychological tests, by doctors. The staff kept them on a rigid schedule as they grew, and cataloged tantrums, naps, and personal squabbles. It was noted that each quint became closest to the fetus with which they had shared an amniotic sac, and that the last quint, believed to have shared a sac with a miscarried twin, was off on her own a lot. It was noted that all except one quint were right handed, and that some had identical swirl patterns in their hair.
Also taking notes were the three million people who came to watch the quints between 1934 and 1943. The children were an international tourist attraction, and either displayed to visitors in matching outfits or watched by them through glass. Gift shops sold post cards, and across the street, their father sold souvenir postcards.
Their parents fought a long legal battle to get the quints back. They didn't succeed until the kids were eight years old. At that point, the five girls were a marketing phenomenon, and their parents sold their images to decorate oatmeal and maple syrup packages, and toured the girls around in identical dresses, making appearances. By all accounts, the girls had to shoulder most of the chores at home, while their images provided the entire family with money that they never saw.
It's not surprising that as soon as the quints reached maturity they split up, and each attempted to live quiet lives relatively separate from both their parents and each other. Decades later, the Prime Minister traveled to make a personal apology, and give a monetary settlement, to the two remaining quintuplets.
Top Image: Library and Archives Canada