It’s become a persistent critique of former Secretary of State Hillary Rodham Clinton’s presidential campaign, but at the time she uttered her famous “what difference … does it make” about the Benghazi terrorist attack to Congress in 2013, her inner circle thought she’d hit it out of the park.

“Great answer,” wrote one admirer. “She was incredible today,” another chimed in, as her own team gave each other virtual “high-fives,” believing they’d not only escaped a political trap but had demolished Sen. Ron Johnson, the Wisconsin Republican who provoked her fiery — and now infamous — retort.

Mrs. Clinton’s intense preparation and the post-showdown crowing from her team are all detailed in the latest batch of more than 5,000 emails from Mrs. Clinton’s time as secretary, which the department released Monday in response to a court order.

Of the new messages, some 325 have information now classified as “confidential” and one has information deemed “secret” — for a classification rate of 6.3 percent. That’s the highest rate yet of any of the six monthly batches, dating back to June, when just 1.1 percent of her emails contained information not appropriate for public view.

“With the number of emails containing classified information now numbering nearly one thousand, this latest court-ordered release underscores the degree to which Hillary Clinton jeopardized our national security and has tried to mislead the American people,” Republican National Committee Chairman Reince Priebus said in a statement.

Most of the classified messages were exchanged with fellow State Department employees, but a few of them were between Mrs. Clinton and former British Prime Minister Tony Blair, and others involved Sidney Blumenthal, a controversial confidante of the Clintons.

Mr. Blumenthal was one of the most enthusiastic commenters on Mrs. Clinton’s Jan. 23, 2013, appearance before Congress to try to clear the air on her role in the Benghazi terrorist attack, which left four Americans dead, including the U.S. ambassador to Libya.

He urged Mrs. Clinton to “always wear the glasses” — a reference to the spectacles she donned after suffering a concussion and blood clot that left her with vision problems in late 2012. Mr. Blumenthal then went on to call her Republican questioners “cretins and reptiles,” and predicted that female voters would punish the GOP for asking tough questions.

Mrs. Clinton made headlines with her combative reply back to Mr. Johnson, who prodded her on why the administration misjudged the reasons for the attack.

“What difference, at this point, does it make?” the former first lady and senator retorted. Her team thought it the right response, but much of the rest of the country disagreed, and the phrase has become a refrain in GOP attacks on Mrs. Clinton.

One discordant note came from former Clinton pollster Mark Penn, who in an email the night of the testimony told her to cool it: “I don’t think the emotion in the hearing works to your advantage — looks more like they rattled you on something no one outside the crazy right blamed you for anyway,” Mr. Penn said.

Mrs. Clinton’s inner circle disagreed, saying she “looked real.”

The new set of emails included messages from 2011, 2012 and 2013 — years that hadn’t been well represented in previous releases, but are in many ways more relevant to her current presidential campaign.

Among the revelations was that Mrs. Clinton lost email service for two weeks after Hurricane Sandy struck New York, knocking out the email server she kept at her home in Chappaqua. In a message to a friend in Illinois in mid-November, Mrs. Clinton apologized for having been off the grid, blaming the storm for “losing my internet/[Black]berry service.”

Her unique email arrangement sparked a furor that has lasted most of this year. By refusing an official State.gov account and using the server she herself set up, Mrs. Clinton shielded her messages from review by public records requests during her entire time at the State Department.

She also didn’t turn the messages over when she left in early 2013, waiting until she was prodded by the congressional probe into the Benghazi terrorist attack to finally relinquish more than 30,000 messages.

Some of her top aides have also acknowledged they too used non-State.gov accounts to conduct government business, in violation of department policies, and have had to go back and relinquish tens of thousands of their messages.

Mrs. Clinton’s email messages are all being released publicly, while her aides’ messages won’t be released in full, but are being searched in response to dozens of open records requests.

The Associated Press, which filed one of the requests seeking Mrs. Clinton’s schedules, reported Monday that she met or spoke by phone with nearly 100 corporate executives and longtime financial backers in what the news organization described as stark planning for the 2016 campaign even while she was still holding office under Mr. Obama.

The Associated Press said it has not found any ethical or legal conflicts in the meetings.

The State Department has now released about two-thirds of Mrs. Clinton’s emails, with two more releases to come — one at the end of December and another at the end of January, or just days before the Iowa presidential caucuses.

The messages provide an unparalleled look into the former secretary’s life, depicting someone not entirely comfortable with technology.

In one message to an assistant she asked for a printout of an article from The Washington Post, but sent the URL for the paper’s online front page instead. Her assistant had to ask if there was something in particular she’d meant to ask for.

Mrs. Clinton’s deep ties with Mr. Blumenthal are also on display in the new batch of emails. In one message after the Benghazi attack but before her public testimony, Mr. Blumenthal gave her advice on how to handle the growing questions: “Publicly and directly puncture conspiracy fever on Benghazi before any closed hearing, in response to press question that you make yourself available to.”

He also advised her on peace negotiations in Northern Ireland, and in one instance Mrs. Clinton even gave Mr. Blumenthal marching orders, asking him to confirm details he had shared with her about one of the factions involved in the peace negotiations.

Mrs. Clinton had previously said Mr. Blumenthal’s messages to her were unsolicited.

All told, of the 21,360 emails now released, 991 of them have information redacted as “confidential” and five had information withheld as “secret.” One of those secret documents was new in Monday’s batch — a copy of an email released during the initial set of Benghazi-related messages.

Mrs. Clinton has insisted none of the information was classified at the time she sent it. The FBI is reportedly investigating to see if any information was mishandled.

The classified documents are routinely marked as relating to information derived from a foreign government or concerning a foreign power’s activities, which would cover messages such as Mr. Blair’s.

One document simply labeled “PLAN” was redacted entirely, including the name of the author and the date of the document. And another document, which the department filing system listed as a letter from Israeli Prime Minister Benjamin Netanyahu and addressed to “President,” was also redacted in full.

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