How did scientists conclude that the expansion of the universe seemed to be slowing down until around 5 billion years ago?

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Just been on a space video kick lately and am pretty ignorant about most of it.

One thing I see a lot of these videos saying is that the expansion of the universe seemed to be slowing down until around 5 billion years ago.

How can we tell that it was slowing down 5 billion years ago if it started speeding up afterwords? Like how do they map out the universe and say “yeah it was slowing down until this time.”

Is it just a theory or is this something commonly accepted as fact? Appreciate any info and thanks! 🙂

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