Wait then what about events that happen on Pluto?

Pluto is around five light hours away from us.

If an astronaut goes to Pluto and films herself doing activity A and then broadcasts that back to Earth, it would take around five hours for the broadcast to reach us.

So you’re saying that it is not correct to say her recorded activity happened five hours ago?

The idea driving this conclusion is called the Relativity of Simultaneity - There is no absolute notion that two events happened "at the same time". You want to say that a distant event occurred at the same time as a nearby event that occurred 5 hours ago. However, a distant third party observing both events would not agree.

This becomes painfully apparent when dealing with black holes. Person A falling into a black hole passes through the event horizon normally and reaches the singularity in finite time. However, Person B observing from outside never sees Person A pass through the event horizon. From Person B's perspective, it doesn't make sense to ask what happens simultaneously with Person A reaching the singularity - it takes infinite time just to reach the event horizon. Even asking the question is nonsense.

https://en.wikipedia.org/wiki/Relativity_of_simultaneity

If we imagine a third observer in a space craft traveling close to he speed of light, it's possible to construct the scenario in such a way that the pilot of the space craft would observe the two events happening at the same moment. Time is relative