What do the Fifth House actually do?
Sure, yes, ghosts and tradition and the Heart of the Emperor, and Watchers Over the River - but none of those things give you the kind of assets that mean you can dress your cavalier in a coat that "probably cost more than the Ninth House had in its coffers" for a dinner party.
It's made clear very early on that the Fifth are a power to be reckoned with. When they first receive the letter about the Lyctoral pilgrimage, Gideon assumes it would be on the Third or Fifth. Harrow, meanwhile, has frequently-repeated anxieties about the Ninth being subsumed by the Third or Fifth, to the point that she worries that the anniversary party invitation may be an attempt to wipe out the other Houses. Teacher describes the Fifth's relationship with the Fourth as "hegemonic". The Fifth loom so large in the cultural imagination, they even inform the name of the made up porn magazine that Gideon offers to Crux.
The links between the Third and the Fifth that both Gideon and Harrow make seem to reflect both the fact that these two Houses have particular power and influence, but also that they frequently cooperate. Judith writes about the close cooperation of the Second, Third, and Fifth, a relationship which becomes a source of tension as the scions seek to establish authority after the Fifth are murdered. Judith says:
“The Fifth are dead. I take authority for the Fifth. I say we need military intervention, and we need it right now. As the highest-ranked Cohort officer present, that decision falls to me.” “A Cohort captain,” said Naberius, “don’t rank higher than a Third official.” “I’m very much afraid that it does, Tern.” “Prince Tern, if you please,” said Ianthe.
Which makes it sound as though Abigail might technically have been considered the highest ranking person at Canaan House (likely because she was head of her House and not an heir in waiting like Judith or Coronabeth), and that following her death there is some question as to whether the Second or the Third should take control, but notably no suggestion that anyone else might.
We know what the Second do: they are the leaders of the Cohort and the Bureau, the military and intelligence that forms the core of imperial expansion. Most of the information that we get about the other Houses talks only about their cultural or ritual roles in the empire - we get very little in the way of gritty details of what happens outside of the Dominicus system.
We know a little bit about what the Third does - according to Tor they are cultural trendsetters and players in soft power, but the one detail we get in GTN itself is revealing: when Gideon imagines her glorious future in the Cohort, one of the assignments she considers boring is the prospect of being "in some foreign city babysitting some Third governor." Which makes it sound rather like the Second are conquering the planets and the Third are then running them. But the books are even lighter in details about what the Fifth do, beyond ghosts and manners.
However, there is one suggestive detail: an important topic in HTN is stele travel - the necromantic FTL used by the Nine Houses. And Mercymorn, in describing a stele, specifically states that Fifth House adepts are required for their construction. Which rather makes it sound like the Fifth have a monopoly on the manufacturer of the technology required for FTL travel. Now that in and of itself could be the basis of their enormous wealth - selling aerospace tech to an ever expansionist military is probably quite lucrative.
But there's another element of House imperialism that only gets mentioned in passing that doesn't seem to be entirely accounted for, which Judith describes in As Yet Unsent:
"Their other line of attack is the business contracts. They claim that the services asked of them by the Emperor were set down in lifetime contracts by previous generations, who assumed the contracts would be terminated upon the Emperor’s death."
There are obviously some unanswered questions about the imperialist project of the Nine Houses - both Augustine and Coronabeth question quite why it works the way it does - but from the above it sounds like in many respects it functions exactly as you would expect an empire to: as a vehicle for the exploitation of others' resources.
Perhaps the Cohort themselves administer these business contracts. Perhaps they fall under the purview of the Third House planetary governors. But if you're exporting resources from the living planets of your empire to the mostly desolate planets of the Dominicus system, you're going to need some FTL ships and a whole lot of bureaucracy.
And if there's one other detail that we get about the Fifth, it's that there is something significant about the political power of their bureaucracy. As Judith puts it: "Quinn himself is a Fifth House bureaucrat with all that entails."
Are the Second, Third, and Fifth so close and so powerful because they form the bedrock of the empire: the conquest, control, and exploitation of planets beyond the Dominicus system?
