Based on the “Jackdaw is a crow” copypasta by Unidan, the pasta has been adapted for Halo.
Here's the thing, you just said Halo 5 is a Halo game.
Is it in the same franchise? Yes. No one's arguing that.
As someone who is a MLG Pro who studies Halo, I am telling you, specifically, in the MLG circuit, no one calls Halo 5 Halo. If you want to be 'specific' like you said, then you shouldn't either. They're not the same thing. If you're saying 'Halo Franchise' you're referring to the Microsoft IP, which includes things from Halo Wars to Halo 2 to Halo 4. So your reasoning for calling Halo 5 a Halo game is because random people 'call the shooter game with sprint a Halo game?' Let's get Call of Duty and Battlefield in there, then, too. Also, calling someone a Halo 2 player or a Halo 3 player? It's not one or the other, that's not how Halo works. They're both. Halo 5 is Halo 5 and a member of the Halo franchise. But that's not what you said. You said Halo 5 is a Halo game, which is not true unless you're okay with calling all shooters with sprint Halo games, which means you'd call CoD, Battlefield, and other games Halo games, too. Which you said you don't.
It's okay to just admit you're wrong, you know?