Is Smash Ultimate the 5th or 6th Game in the Smash Bros. Series?

Sixth

According to Sakurai it is the sixth because in an interview in 2013 he refers to Smash for Wii U and Smash for 3DS as "versions four and five within the series".

Sakurai: No, actually, there was never any consideration to having him in previous games, and if you think about it, there hasn't been really a precedent for third-party characters joining other than very special cases like Sonic, during the last game. It's something that wasn't even possible. We're now going into versions four and five within the series—this is only something that's now possible.

Kotaku: When you say four and five, do you mean the 3DS and Wii U versions? Those are separate?

Sakurai: Yeah, exactly.

Kotaku: While we bring that up, how will those versions be different?

Sakurai: Essentially between the two versions the character structure is the same, and the moves shared between the characters are the same, but the stages are entirely different. On the 3DS, we've taken the motif of handheld games and then on the Wii U version, featured primarily stages based on games on console.

Kotaku: And how will they be able to connect, the 3DS and Wii U version? Will I be able to play against Wii U people if I'm using the 3DS?

Sakurai: It'll be possible, in fact, on the 3DS version there'll be a certain degree of character customization. You can have your own personalized character that you'll then be able to take over and move onto the Wii U version and play.

Kotaku: And you can also—on the 3DS version—play against people playing the Wii U version?

Sakurai: Actually, that's not possible. What is possible is for you to be able to customize your character, transfer it to the Wii U, and then play there. It would be technically impossible, just because the stages are so different between the two versions, so there isn't a situation where you have a handheld device and a console and you're able to play at the same time. Just more of a situation where there's integration, and [ability] to transfer data.

_{Kotaku, An In-Depth Chat With The Genius Behind Super Smash Bros.}

While I personally prefer to consider it to be the 5th game, technically it is the 6th, because 5 other entries came out prior to it. The confusing thing is that Super Smash Bros for 3DS is the 4th game and Super Smash Bros for Wii U is the 5th game, because they came out at different time, and although the games are practically identical, they have some differences, so they are considered separate entries. N64 is 1, Melee is 2, Brawl is 3, 3DS is 4, Wii U is 5, and Ultimate is 6.