Xbox One's Halo title is indeed a "legitimate" entry in the series, according Microsoft game studios VP Phil Spencer, also noting that the franchise is now considered a "saga" instead of a separate set of works.
Speaking with GameSpot during E3, Spencer wouldn't be drawn on whether it the game is Halo 5, whether it will contain a different subtitle, or not one at all; instead saying the firm will talk more about the story arc and "how it plays out" at another time.
"Having [producer Bonnie Ross] come out [at E3] and announce the game, making sure people know it's a legitimate version of Halo coming out, and when it's coming out, and features that they're focused on we thought was…important," Spencer said.
Halo 4, was at one point the start of the Reclaimer Trilogy, with Halo 6 concluding the trilogy, but a Microsoft representative confirmed to Gamespot this is no longer the case
"While we originally said trilogy, we've actually expanded this to more of a saga, so we don't want to limit the Reclaimer story within a trilogy," said the rep.