The lore, as I recall it, tells us that Midgardsormr came from another star, and once it arrived, it produced its first brood. In ARR we hear the first mentions of Nidhogg, and in early Heavensward we learn of Hraesvelgr and Ratatoskr (sp?). As we reach Azys Lla, we meet Tiamat and learn that she and the real Bahamut, not the primal, were also among the first brood, and it is mentioned that the first brood totaled 7 dragons. I don't recall these last 2 dragons being named. If Shinryu is as Bahamut, then that would make 6, but I don't recall ever getting that information, so that's merely speculation on my part.

The wiki entries I've read on the subject also only mention the 5 I know to be confirmed