As dramatic as it may sound, the 5000 figure may understate just how much life is going on in Zaatari. UN officials estimate that the total number of births for those in the camp is closer to 10,000; a number of nongovernmental organisations offered childbirth facilities before the clinic opened in 2013, and over 1000 cases that required more advanced medical techniques have been referred to a nearby hospital run by the Moroccan military.
Zaatari's population surged in the early years after the fighting started, at one point soaring to more than 100,000 people - enough to make the camp the fourth-largest "city" in Jordan.
After many families moved to escape the crowding and live outside the camps, the population dropped to around 80,000. Now, many argue that the camp is getting better and better - and that it may even evolve into a real city within a few years.
"They have created something that is approaching normalcy," Aoife McDonnell, the UN refugee agency's Jordan spokeswoman, said of the refugees in the camp.
At the event on Tuesday, Rima's father showed off some of that normalcy, bringing plates of falafel from the restaurant he works at in the camp to pass out to guests. Mohammed Salameh, 22, argued that the falafel is the best in Zaatari. He may well be right, but there is plenty of competition: Zaatari's central street, dubbed the Champs-Elysees, is full of places to eat. There are estimated to be thousands of small businesses operating in the camp, with shops selling wares as varied as wedding dresses and bicycles.
Back in a small trailer that Salameh shares with his extended family, it is clear that while things may have stabilised in the camp, the problems are far from over.
Salameh says he earns just five Jordanian dinar a day for a 12-hour shift at the restaurant, barely US$7. Over the course of the month, he makes around US$210, a figure that is stretched extremely thin as he is the sole bread winner for his large extended family.
Despite the new start in Zaatari, the family still faces daily challenges. Salameh's father, who suffered a stroke, needs medical attention. One of his daughters was killed in a barrel bomb in Syria. Her infant son, Fahad, now lives with Salameh in Zaatari; the family says he survived in the rubble for hours before being found. Another of Salameh's sisters has a young child named "Sham," the Arabic word for Syria - the homeland where new mother Kholoud Suliman's entire family remains, despite the risk and the distance from their daughter.
In the end, Salameh explained, the hope is that Rima and her sister won't go through all this. What he and his wife want for their daughters is just "a better chance than we did in our lives."