I think Sector is a pretty solid name for the collection of the 5, though I think Industry might work too. It's not very sci fi sounding, though. Depending on the type of lore you're trying to build, having each of them as a Ministry (or Division) might help establish the world ("Ministry of Agriculture", etc.). Again, though, not especially sf sounding. A quick flip through my thesaurus gave me Stratum (plural would be Strata), which sounds sorta neat. Lamina (Laminae) is a term used in botany/geology used to describe layers, which also sounds pretty sf.
Agriculture is a common enough word that most people will know immediately what that sector does. Cultivation sounds a little more exotic, and is pretty much just as common of a word. Agrology is the science of crop-growing, and, while not especially common of a word, it's meaning can probably be inferred from it's similarities to Agriculture.
Mining is another solid term, because everyone knows what it means. Excavation comes to mind. Something might be able to be done with farm terms like Harvest, but something like Mineral Harvest sounds pretty silly (like a breakfast cereal lol). idk Excavation seems ok
I'm not a huge fan of Industry, and agree with you that Manufacturing seems like a better title, whether or not you call them all Industries. Fabrication might also work.
I like Refining (though Ministry of Purity or something sounds really metal lol). Words with similar meanings include Distill (Distillation), Filter (Filtration), Rarefy (Rarefication isn't a word but hey this is sf do whatever you want. Technically it'd be Rarefying, I think).
I'm not fond of Administration either, but it seems to fit the set of stuff you want to encompass. Obvious alternatives are Government (or Governance), Bureaucratic or Legislation, but I don't think that's what you're looking for. Empire or Regime both sorta fit but not really. idk this one's tough