SOUTH BEND, Ind. — In the moments after a convincing victory, a housekeeping item seemed important. Hey Brian Kelly, are you ready to name Ian Book your starting quarterback?

Notre Dame’s coach stopped at our question — “I haven’t named him?” — but of course he had not, and he knew it. The official depth chart Saturday against Stanford read:

“BRANDON WIMBUSH

or Ian Book”

It made little sense going in — and none coming out. After a 38-17 victory, this much is certain: Book is Notre Dame’s quarterback. And this might not be too much:

With Book at quarterback, Notre Dame has the look of a legitimate contender for the College Football Playoff.

“I think it’s starting to come together,” Kelly acknowledged, before adding: “Man, we’ve got a long way to go.”

More:10 observations from Week 5 in college football

More:Winners and losers from Week 5 headlined by Clemson's close shave

He’s right, of course. We’re less than halfway through the season, and drawing deep meaning from college football’s weekly momentum swings is a fool’s game. But Notre Dame is 5-0, and the Irish have come a long way in the last two games.

Officially acknowledged or not, Kelly’s decision to replace Wimbush with Book has jump-started the offense. After scoring 24, 24 and 22 points in their first three games, the Irish have scored 94 points in the last two games. It’s evidence of the “sense of urgency” Kelly says the junior quarterback has injected into the Irish attack.

“There’s an energy that he brings,” Kelly said.

A moxie, too. And according to receiver Miles Boykin, a calm and poise that breeds confidence. But tangibly, Book has brought a passing game to Notre Dame.

The 6-0, 203-pounder does not make anyone’s eyes pop, but he’s filling up the stat sheet. After throwing for 325 yards and accounting for five touchdowns against Wake Forest, he was 24-of-33 for 278 with four touchdowns against Stanford. He made plays and avoided mistakes.

One moment that ultimately didn’t matter to the outcome illustrated Book’s "it" factor. With the lead in the final minutes, Notre Dame was chewing clock. On third down, Book scrambled left away from pressure. It looked as though he might tuck and run. Instead, he suddenly uncorked something resembling an option pitch — only it was downfield, over a defender’s head and into the arms of running back Jahmir Smith for a first down.

“I’m just trying to bring the tempo and personally get those guys to ride behind me,” Book said. “To work faster on offense. To bring some juice and be a leader.”

More:Ohio State escapes Beaver Stadium with dramatic victory over Penn State

More:Texas A&M coach Jimbo Fisher yanks his player by facemask after scuffle

To clarify, we asked again — mostly for fun — is Book the starter? Kelly didn’t say. But he didn’t need to. We all read what happened between the lines.

As the passing game has sprouted, the running game has benefited: 272 yards on 55 attempts, led Saturday by Dexter Williams, who returned from a four-game suspension for undisclosed reasons to rush for 161 yards, including a 45-yard touchdown on his first snap of the season.

“We just want to be an elite offense,” Book said, adding: “We just want to keep scoring points.”

It’s very possible Notre Dame would still be undefeated with Wimbush as the starter. He’s 13-3 in that role, a senior leader whose running often offsets a limited passing ability. Meanwhile, the defense is good enough to keep the Irish in games. Saturday night, they made Stanford one-dimensional, holding the Cardinal to 55 rushing yards on 24 attempts — star running back Bryce Love had 73 yards on 17 carries, with 39 of those coming on one run — and sacked K.J. Costello five times.

But with the offense’s sudden potency, the ceiling has risen.

“I couldn’t tell you where our ceiling is, honestly,” said Boykin, who had 11 catches for 144 yards and a TD. “If we play like this for the rest of the season — obviously we played well tonight, but we can get a lot better. It’s almost scary to think about what we can do.”

All of which takes us to the bigger picture, and to Notre Dame’s potential. Looking at the schedule, it seems more than possible the Irish won’t face a more difficult test the rest of the way; several dates that in the preseason looked prickly don’t seem as daunting.

But don’t try to suggest it to Kelly. Unprompted, he noted a game next week at Virginia Tech. And the one after that against Pittsburgh. And the one after that against Navy. And the one after that against Northwestern. (He stopped there rather than list Florida State, Syracuse and USC.)

“We’ve got a long season ahead of us,” he said, “so if we’re gonna walk out here thinking that we just are the best team, we’re gonna get beaten and it’s gonna diminish this victory.”

Kelly likened the remaining schedule to “climbing Mount Everest,” which seems a little much. Given what we’ve seen so far from the upcoming opponents — and these last two games, from Notre Dame — it looks not only manageable, but maybe even favorable.

Which means the Irish should be in the Playoff conversation now. If they keep winning, the idea they could take one of the four slots will make fans of other contenders very uneasy. Along those lines, so should this:

“I still think we can hit another level,” Boykin said.

They’d need to, of course, if those fans chanting “We want Bama!” after the game actually got their wish. But if Notre Dame has a long way to go, it’s starting to come together.

And with Book, the next few chapters promise to be very interesting.