Five teenage boys who say they were molested by former U.S. House Speaker Dennis Hastert.

That is the dark secret the feds say led Hastert to agree to pay one victim $3.5 million so others wouldn’t come forward, federal prosecutors said Friday in a sentencing memorandum.

It’s a secret that cost the once-powerful Republican $1.7 million in payouts — along with his reputation. The memo offers a damning account of the sexual abuses for the first time in a case that’s been shrouded in mystery.

Feds say Hastert molested a 14-year-old boy — the Individual A who sparked the investigation — and then, decades later, gave him hush money. And when feds investigated the payments, Hastert tried to turn the tables on the victim, claiming extortion.

Much of the abuse happened in a Yorkville High School locker room. There, as a wrestling coach, prosecutors allege, Hastert sat in a “Lazyboy”-type chair and watched the boys shower. Another incident of sexual abuse happened in a motel room during a wrestling camp, where one wrestler was singled out.

The new details come as the ailing Hastert awaits sentencing on April 27. Hastert, 74, has pleaded guilty only to a financial crime — the statute of limitations for any sexual abuse charges has long passed.

But prosecutors say the sexual abuse has deeply affected the lives of the victims, even into adulthood.

“He made them feel alone, ashamed, guilty and devoid of dignity,” Assistant U.S. Attorney Steven Block wrote. “While defendant achieved great success, reaping all the benefits that went with it, these boys struggled, and all are still struggling now with what defendant did to them.”

The document details the account of four victims, all wrestlers. Stephen Reinboldt, who died in 1995, was a student manager for the wrestling team. He told his sister about the abuse before his death.

Prosecutors say Hastert’s sexual abuse of boys was still happening when he chose to enter public life in October 1979.

“Defendant was so sure his secrets were safe that he apparently had no fears about entering a profession where one is subject to constant scrutiny and media attention,” prosecutors wrote in the memo, which said the government is seeking a sentence “within the applicable guidelines range,” and that range allows for a prison term of anywhere from zero months up to six months in prison.

The extortion helped feds unravel the abuse. Individual A met with Hastert in 2010, decades after the abuse, and asked for $3.5 million in payments. After monthly meetings, they arranged to meet every three months with Hastert handing out $100,000.

The payoff was spotted by the bank in April 2012, as they noticed unusual account activity — seven $50,000 cash withdrawals between June 2010 and April 2012 at a branch in Yorvkille. In total, the feds say Hastert paid the man $1.7 million.

After talks with the bank, Hastert stopped withdrawing $50,000 and instead withdrew cash in $9,000 increments until the bank closed his account in February 2013.

That’s when Hastert decided to turn on the victim. He called the FBI and said he was being extorted, based on the false claim of a former Yorkville High School student and wrestler.

The government soon began connecting the dots. In two recorded phone conversations, authorities noticed the man on the other line didn’t sound like he was being extorted. The victim spoke of the importance of keeping everything private because it was personal.

Those calls led the feds to interview the victim, who detailed the sexual abuse. He said Hastert molested him during a wrestling camp trip. The victim said he stayed in Hastert’s room while the other boys stayed in another. He didn’t know why Hastert “singled him out” and said he was touched inappropriately when he told his coach about a groin pull.

When the victim confronted Hastert in 2010, he asked him why he had done it. Hastert said “it was a confusing and difficult time in his life,” prosecutors wrote.

Another victim, identified as Individual B, was 14 at the time of the abuse and was molested on a table when Hastert told him he could “loosen him up.” As the teen turned on the table, Hastert “performed a sexual act” on him, the document says.

A victim identified as Individual D told the feds Hastert would sit in a chair and watch the boys shower. When he was 17, Hastert told him to lie face down on a table and performed a sexual act on him. Another victim said Hastert inappropriately touched him after he offered him a massage.

Hastert hasn’t publicly acknowledged the allegations, even filing a motion Friday that suggested he is still not ready to do so.

Lawyers for Hastert on Saturday released a statement saying Hastert “earnestly apologizes” to those he’s hurt. They also noted that Hastert had “made every effort to be a positive force in the lives of others,” within the last four decades.

“Mr. Hastert acknowledges that as a young man he committed transgressions for which he is profoundly sorry,” attorney Thomas Green said in the statement. “He earnestly apologies to his former students, family, friends, previous constituents and all others affected by the harm his actions have caused.

Green’s statement echoes what he wrote in a sentencing memo filed on Wednesday, which asked the judge for probation.

Hastert Sentencing Memorandum