Cooperstown is getting more crowded this summer, but just five votes more and Billy Wagner would have been joining the party.

Adrian Beltre, Todd Helton and Joe Mauer were all elected into the Baseball Hall of Fame on Tuesday, each surpassing the necessary 75 percent of the vote from the Baseball Writers’ Association of America.

Beltre (95.1 percent) and Mauer (76.1 percent) both got in on their first years on the ballot while Helton (79.7 percent) got over the hump in his sixth year.

Wagner, the former Mets closer, fell just five votes short (73.8 percent) in his ninth year on the ballot, though he figures to have a strong chance of getting in next January in his 10th and final year.

“In a little way, it’s a gut-punch, but on the other hand, you’re still on the ballot,” Wagner said by phone on Tuesday night. “It’s one of those things that for me, I feel like, it’s just kind of the epitome of what my life has been like in a nutshell.

Saying, ‘Hey, it’s gonna come down to the very end,’ and we’ll just see how it goes. But I can’t complain. Gosh, I’m still on there. There’s 70-whatever percent that still like me. But it’s tough.”

Adrian Beltre cruised into Cooperstown in his first year on the ballot.Neil Miller

Former Yankees outfielder Gary Sheffield came up 43 votes shy (63.9 percent) of induction in his 10th and final year on the BBWAA ballot.

If the nine-time All-Star is going to find his way into the Hall of Fame one day, it will have to be through a future veterans committee.

The 2024 class — along with former manager Jim Leyland, who was voted in by the Contemporary Baseball Era Committee last month — will officially be inducted into the Hall of Fame on July 21 in Cooperstown.

While Wagner came painstakingly close to joining them as Hall of Famers on Tuesday, he continued to see his support rise after coming within 27 votes of induction last year.

Still, he wasn’t taking anything for granted in terms of his chances next year.

“It’s difficult and it’s very disappointing right now to sit here and think about next year,” Wagner said after finishing a baseball practice at Miller School in Charlottesville, Va., where he has coached the varsity team the last 12 years. “Because for me … the first thing they said last year to me was, ‘Nobody’s ever gotten over 60 percent and never gotten in.’ Well, there’s always gonna be that first one.

“In so many ways, I dread having to go through this, but I’ll be honest with you, I can’t say it’s the worst thing in the world. Goodness gracious, I’m on the Hall of Fame ballot. It’s just a tough thing to crack and unfortunately that’s just where I’m at.”

Before Tuesday, the BBWAA had not voted in more than two players in the same year since 2019, when it voted for a four-player class (Mariano Rivera, Edgar Martinez, Roy Halladay and Mike Mussina) for the second straight year.

Todd Helton posted big offensive numbers to go with his Gold Glove defense.Getty Images

Beltre breezed through as a first-ballot Hall of Famer after a 21-year career in which he was a five-time Gold Glove third baseman, four-time All-Star and four-time Silver Slugger with 3,166 hits and 477 home runs.

The former Ranger, Dodger, Mariner and Red Sox, who excelled in the second half of his career, was a lifetime .286 hitter with a .819 OPS.

“I’m proud of the fact that I was able to play for a long time and be able to compete at the highest level,” Beltre said on a conference call. “Whatever comes after that, I was fine with it. This is a great day for me. I’m honored to be in the Hall of Fame. It’s something that I never even dreamed of.”

Helton, who fell 11 votes short of induction in 2023, finally got the call on Tuesday to become the second Rockie to make the Hall of Fame. During his 17-year career in Colorado, the left-handed-hitting slugger was a five-time All-Star, three-time Gold Glove first baseman and won a batting title when he hit .372 in 2000.

He was a lifetime .316 hitter with a .953 OPS, and while his numbers were especially good in the hitter-friendly Coors Field, they were strong on the road as well.

“I think I would use the word ‘validate,’ ” Helton said. “I was talking to my wife and that’s one thing I said: Everything I’ve done, it really did happen and it was good enough to make it to the Hall of Fame.”

Mauer excelled as a catcher before moving to first base.Charles Wenzelberg/New York Post

Mauer cleared the 75 percent threshold by just four votes after being one of the best catchers of his era during a 15-year career with his hometown Twins.

While a concussion forced him to move to first base late in his career, he spent the first 10 years of it behind the plate, winning an MVP, three batting titles and three Gold Gloves.

The six-time All-Star was a career .306 hitter with a .827 OPS and joined Johnny Bench and Ivan Rodriguez as the only catchers to be inducted on the first ballot.

“I definitely don’t take that lightly,” Mauer said. “It’s unbelievable. I’m still kind of pinching myself to receive that type of news.”