In Halo, the campaigns mention seven installations, right? But the Ark is Installation 00, and in the mission where Arbiter kills the Prophet, there are 7 ring holograms. Do they not consider the Ark as a true installation?
Also, this is off-topic, but didn’t they say that the Halo ring in the last mission of Halo 3 is the one made to replace Installation 04? Also, was Installation 05 ever destroyed in Halo 2? Just a couple of things I can’t remember.
The Halo rings are indeed the seven installations. However, the Ark is the control room for all the halo rings. The Ark was designed to fire all the Halo rings in one push of a button. Also, Installation 04’s replacement (referred as Installation 04B) was the replacement for the Halo ring destroyed from the first game.
Installation 05 was never destroyed, when Miranda Keyes pulled out the index from the firing mechanism, the installation put itself into a ‘ready to fire’ type of phase. By doing this, all the Halo rings went into this state. So the Ark was the only thing that could fire them (which is the reason why they go to the Ark in Halo 3)
When the arbiter kills the prophet you are on the ark. The ark is a control station so it has holograms of what it controls.
As for Installation 05
> Aftermath
> When Installation 05 was last seen, the Flood were seen having complete control over High Charity and several of the surrounding fleet. The Great Schism, a civil war between Covenant species, split the empire into Loyalist and Separatist factions. At the end of the battle, what is left of the Sangheili fleet sterilized the installation, most likely by means of glassing the surface.[5] The hologram in the Citadel on Installation 00 shows Installation 05’s surface as completely barren.[6]
And also Minor spoilers, not really a big deal
According to the Foreruner series of books there were originally 2 arks and 12 Halos
> In Halo, the campaigns mention seven installations, right? But the Ark is Installation 00, and in the mission where Arbiter kills the Prophet, there are 7 ring holograms. Do they not consider the Ark as a true installation?
>
> Also, this is off-topic, but didn’t they say that the Halo ring in the last mission of Halo 3 is the one made to replace Installation 04? Also, was Installation 05 ever destroyed in Halo 2? Just a couple of things I can’t remember.
You’ll probably get better feedback in the Halo Universe section. Hopefully a mod will move this thread and you’ll have more luck 
That said;
There is more than one ark. Because the ark isn’t a halo itself, I imagine that it would be labeled differently.
As for the 5th halo, last I recall the Delta halo got overrun by the flood.
There were 12 but 5 were destroyed before the forunners could use them.And there are 7 now.The ark is just one of the millions of other forunner installations.And yes the ring at the end of h3 was a replacement.I don’t know why they didn’t replace the other 5.And no delta halo is still intact but infested with flood.Also i believe there were 2 arks.
I’ll break it down.
Installation 00 is one of two Arks, yet this is the Lesser Ark. It makes the 10,000 km long rings we’ve been on. There is a Greater Ark and it was responsible for the original 12 rings that were 30,000 km long. However, those rings could be broken down to be made smaller. So while I’m fuzzy on which rings are which, we now only have 6 rings seeing as how Installation 04 and 04(II) no longer exist.
Installation 05 was sterilized by the Elites, so they probably glassed it.