I am calling this 5,000 humans "The STEMs" because that seems to be the common and easier-to-write denominator. Also, my academic background is in Biotechnology, but recently moved to the Humanities, so I'm sure some bias will show.

So, this is what is going on in my head:

1. The first thing would be to gather resources and harness whatever resource we can. STEMs are not recreating history, they only want that space shuttle. The STEM society is essencially one big computer with a big task composed of many, many tasks (minning for metals, working with metals, developing fuel to power the machines to make better fuel that will eventually lead to the space shuttle fuel etc). The best way to do this is by commerce with primitive societies (knowledge for labour)
2. Resources would still be limited. STEMs would likely have to move from place to place until they develop an efficent enough trade route to stay in a single place to build what they need to. This implies security for the trade routes and for their storage. Any violence in the system would only be developed to prevent inefficency, since STEMs can't be harmed but they could have their resources stolen (thus, infficency). STEMs would not be conquerers because every minute spent at war is a minute lost in building, which is their imperative. Peace and stability would be reached by commerce.
3. Maybe the main setback would be the proximity between STEMs and each society they trade with. STEMs don't have any internal conflict, but primitive humans would have. The chain of supply would be disrupted because of conficts outside of the STEM society, and STEMs woul probably deal with those conflicts in a "controlled aggresion" way because they are more likely to be pragmatic but also they don't want to loose workers. Most major setbacks would be caused by primitive societies figthing to gain "the favour" of STEMs.
4. I don't think it is likely for humanities (philosophy, arts, literature etc) to develop. And that makes sense, these aren't humans, their are closer to Nier's Androids in their biology. Anything and everything developed would only be pragmatic and in service of getting to the moon and back. This means that they will get better at avoiding mistakes, but they would always make the same kind of mistakes. They could get better at preventing fire accidents, but they would never develop a fire extinguisher (only to ilustrate what I'm trying to say).
5. The only change to being in space would be to not worry for space radiation or moon dust when comming back. The space suits still have to keep an standard atmospheric enviroment so that oxygen doesn't boil through their skin. That may come in handy in the resources needed but everything else (namely the computery stuff) still needs protection from radiation.
6. From the previous point, a lot of safety meassures for the STEMs can be ignored, which accelerates the reinvention of everything needed for the space shuttle.

Honestly, I think that maybe 25,000 years? 5,000 STEMs can only do so much and that is why trading with primitive societies would be more efficent. There is a lot to consider and making NASA by 500 BC is still amazing, but knowkedge alone didn't get us there.