Asked why Ben Folds Five broke up back in 2000, bandleader Ben Folds offers a surprising explanation: “Darren [Jessee, the band’s drummer] made a pass at my mom. That just wasn’t acceptable.”

Folds, long known for a barbed sense of humor, is joking, of course, and this skewed worldview is ever present on “The Sound of the Life of the Mind,” the band’s first album in 13 years, out on Sept. 18.

The first track, “Erase Me,” shows that Folds, 45, has matured but still shows flashes of playful anger. “We wanted something up front to make people feel comfortable that we hadn’t gone off a cliff, because a lot of stuff was gonna be different,” says Folds of the song, which contains the line, “Erase me/Do me like a bro and tase me.”

The Five, which also includes bassist Robert Sledge, will perform at Central Park’s Rumsey Playfield on Sept. 14.

While the album does contain mellower touches than the Five’s ’90s releases — such as the much-easier-listening track “Sky High” — Sledge’s fuzztone bass and Folds’ dizzying piano riffs should please those who’ve missed their combination of wry jokes and virtuoso musicianship.

After finding success with several critically acclaimed albums, and a surprise hit with 1997’s “Brick,” a song about a former girlfriend’s abortion, the group disbanded in 2000. “We were tired,” says Folds. “We stayed jet-lagged for three years at one point. The thing that cracked was our patience for being connected to two other people.”

“We didn’t have personal lives,” adds Sledge. “I felt like I was on a runaway train and couldn’t get off with all the touring. It wasn’t a hard decision to make.”

The trio went their separate ways as Folds had twins, briefly moved to Australia, and made solo albums and motley collaborations with William Shatner, Ke$ha, Flaming Lips and Weird Al Yankovic.

The Five reunited in 2008, when MySpace invited them to perform their 1999 album, “The Unauthorized Biography of Reinhold Messner,” for a live-streamed concert. Playing together felt so right that recording a new album was just a matter of finding time.

Following his three-season stint as a judge on NBC’s “The Sing-Off,” Folds now writes more orchestrations than pop songs. It remains to be seen if the Five will be an ongoing concern, but Folds feels that the hiatus had to happen.

“When I listen to the album and think about the process we went through, we needed that time,” he says. “The album is exactly as it should be, and I’m really proud of it.”