It's been more than five years since Marc Hadden, a firefighter in Myrtle Beach, South Carolina, went on the emergency call that would change his life — and his family — forever.

"It was a normal slow day in November," Hadden, 47, told TODAY. "We were sitting down to eat, hadn't had a call all day."

But then they got one — a woman was complaining of severe abdominal pain. When Hadden and the other firefighters arrived on scene, they quickly realized the woman was in labor.

Rebecca Grace Hadden, who goes by Grace, was born on November 14, 2011. Courtesy of the Hadden family

"It was a pretty serious call for us," he said. "We got her on some oxygen, started some IVs and literally as we were getting ready to leave the parking lot in the ambulance, my partner said, 'We're about to deliver a baby right here.' We had no time to prepare. Before we could do anything — we hadn't even cut her clothes — Gracie came right out. Immediately she was handed to me."

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Of course, she wasn't known as Gracie then. Hadden and his wife, Beth, named her Rebecca Grace Hadden after they adopted her; she goes by her middle name.

At the hospital later on the day of Grace's birth, November 14, 2011, Hadden learned the woman, who he believes was homeless, was putting the infant up for adoption. Hadden and his wife, who had been praying for a third child, jumped at the opportunity.

Two days later, they took her home, and in March of 2012 they got full custody of Grace. Today, she is simply part of the family.

Grace fit right in with her family. Courtesy of the Hadden family

"She's amazing," Hadden said. "She takes gymnastics, she's getting ready to start kindergarten next year at the school where my wife teaches. She's a pretty remarkable kid."

She also has two big brothers: Parker, 12, and Will, 14.

"The boys absolutely love her and she loves them," said Hadden, who still works as a firefighter, but now on a volunteer basis.

Now Grace is a happy 5-year-old who loves gymnastics, soccer and hanging out with her brothers. Courtesy of the Hadden family

"Most days it's business as usual, getting Gracie to day care or gymnastics or soccer," he added. "Every once in a while it will hit us, usually when we're out on a date night ... oh my gosh, my wife and I have been together for 15 years, we have three kids now! Sometimes it's a bit overwhelming. Holy cow, this happened overnight, but we wouldn't trade it for anything."

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Grace, now 5, knows her birth story.

"We have never hidden it from her," Hadden said. "If you ask her where she was born, she says, 'My daddy delivered me in the back of an ambulance.' She knows the whole story. I wanted her to know as soon as she was old enough to understand. I didn't want it to be this huge surprise. It still breaks my heart to think of one day having to explain it to her more in depth ... because she doesn't really 100% get it."

Grace with her father, Marc Hadden. "My all-time favorite picture (of us)," he said. Courtesy of the Hadden family

When that day comes, Hadden will surely be there for her.

"Gracie and I have an amazing bond," he said. "We're tighter than thieves."

"She is part of our family and that is absolutely the way it is," he added. "We love her."