Burma counts this the fifth Buddhist council. Saying so takes a position, and it is worth being clear about what the position is, because a number that looks like a neutral fact is doing work here.
To be the fifth, this gathering has to stand in a line whose first four are the assembly after the Buddha's death, the assembly at Vesali, the assembly under Ashoka, and the writing down of the canon in Sri Lanka. That is the Theravada line as the Sri Lankan chronicles tell it, and Burma had inherited it along with the canon. Adding a fifth to it is a claim about continuity: that a Burmese king in 1871 is doing the same thing an Indian emperor did in the third century before the common era, and doing it with the same authority.
The other Theravada countries did not all take the number up. Sri Lanka and Thailand had their own royal recensions and their own claims to be the guardian of the canon, and none of these traditions had an authority above them that could rule on whose count was correct, because Buddhism has never had one.
None of this makes the council less real or the slabs less remarkable. It does mean that when a source says the fifth council, the useful next question is whose fifth. The atlas records the ordinal as the label a particular tradition uses and describes the assembly by what it did, which is the only way to hold several traditions at once without silently adopting one of them.