WASHINGTON - Most of the reaction to Sgt. Bowe Bergdahl's release after five years as a captive of the Taliban has been celebratory, but a pair of lawmakers questioned whether the deal reached with the Taliban was legal and whether the price paid was too high.

The Army sergeant was held captive for nearly five years by the Taliban, mostly in Pakistan, U.S. officials believe, and the president, Defense secretary, secretary of State, chairman of the Joint Chiefs, and the sergeant's parents all expressed relief and gratitude after 18 Taliban handed Bergdahl over to U.S. special forces in Afghanistan, spiriting him back into the care of the U.S. military.

Two senior Republican lawmakers, however, accused Obama of violating the law by failing to notify Congress 30 days before the deal to swap five members of the Taliban held at Guantanamo and voiced concerns that the U.S. gave up too much.

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The top Republicans on the House and Senate armed-services committees cautioned that "we must carefully examine the means by which we secured [Bergdahl's] freedom," warning that the U.S. had effectively reneged on its policy not to negotiate with terrorists.

So what exactly did the U.S. give up to get Bergdahl back?

The U.S. has released five Taliban prisoners kept at Guantanamo Bay - all of them either senior Taliban figures or Taliban officials with connections to Taliban leaders, and all labeled by the Pentagon as highly dangerous to the security of the U.S. and its allies if released. They are:

• Mohammad Fazl, the former Taliban defense minister during the U.S. invasion of Afghanistan, chief of staff of the Taliban army, and commander of its 22nd Division. According to a U.S. Department of Defense document obtained by Wikileaks, Fazl is believed to be an associate of Supreme Taliban Commander Mullah Omar and was "wanted by the UN for possible war crimes including the murder of thousands of Shiites," surrendered to the Northern Alliance commander Gen. Dostum in November 2001.

  "Detainee is assessed to be a HIGH risk, as he is likely to pose a threat to the US, its interests, and allies," his Guantanamo detainee file reads. "If released, detainee would likely rejoin the Taliban and establish ties with ACM [anti-coalition militia] elements participating in hostilities against US and Coalition forces in Afghanistan."

• Mullah Norullah Noori, a former Taliban military commander and Taliban governor of two Afghan provinces, who led Taliban forces against U.S. and coalition troops and was also "wanted by the United Nations (UN) for possible war crimes including the murder of thousands of Shiite Muslims" as Fazl was, according to Noori's Guantanamo prisoner file as obtained and posted by Wikileaks. He is also believed to be associated with Supreme Taliban Commander Mullah Omar.

  Noori commanded the Taliban in the northern city of Mazar e-Sharif. Like Fazl, he surrendered to Gen. Dostum in 2001.

  Rated a "HIGH" threat to U.S. security interests if released, Noori is or was associated with members of al Qaeda, the Islamic Movement of Uzbekistan, the Libyan Islamic Fighting Group, and Hezb-e-Islami Gulbuddin.

• Mohammed Nabi, another senior Taliban official with ties to al Qaeda, the Haqqani Network, Hezb-e-Islami Gulbuddin, and other anti-U.S., Taliban-allied groups, according to his Guantanamo Bay file as posted by Wikileaks.

  Also rated as a "HIGH" security threat if released, Nabi fought with the mujahideen against the Soviets. After that, he told the Americans who captured and detained him, he was an off-and-on Taliban member in the early 2000s, worked for the chief of the Taliban's Border Department, which controlled smuggling. In early spring of 2002, he left the Taliban to sell used cars in a small village near Khowst and became a CIA informant.

  According to his Defense Dept. file, Nabi was involved in attacks against U.S. and coalition forces and facilitated smuggling routes for the Taliban and al Qaeda.

• Khairullah Khairkhwa, a direct associate of Osama bin Laden according to his Defense Dept. detainee file obtained by Wikileaks, and a senior Taliban military commander who also served as the Taliban's minister of Interior and the governor of Herat.

  He represented the Taliban at meetings with Iranian officials seeking to support actions against U.S. and coalition forces after the Sept. 11 attacks, according to the document. He attended a meeting at the direction of bin Laden, reportedly accompanied by members of Hamas, the document says, and is believe to have been one of the major opium lords of western Afghanistan.

  In 2002, he sought to negotiate an integration into the new government through Wali Karzai, the brother of Afghan President Hamid Karzai who has been accused of corruption and drug smuggling, but was arrested by Pakistani border patrol and released by Pakistan into U.S. custody.

  He is also deemed a "HIGH" threat if released.

• Abdul Haq Wasiq, the Taliban's former deputy minister of intelligence, had direct connections to Taliban leadership and was "central to the Taliban's efforts to form alliances with other Islamic fundamentalist groups" to fight against U.S. and coalition forces, according to his Defense Dept. file obtained by Wikileaks.

  He also used his position to support al Qaeda, assist Taliban personnel in eluding capture, and arranged for al Qaeda members to train Taliban intelligence staff, according to the file.

  He seems to have later turned informant, as his file notes that Wasiq was arrested after a meeting with two Americans and a translator, in which he was supposed to deliver information leading to the capture of Mullah Omar. Shortly after the meeting, U.S. forces arrested him.

"Trading five senior Taliban leaders from detention in Guantanamo Bay for Berghdal's release may have consequences for the rest of our forces and all Americans. Our terrorist adversaries now have a strong incentive to capture Americans. That incentive will put our forces in Afghanistan and around the world at even greater risk," said House Armed Services Chairman Howard P. "Buck" McKeon, R-Calif., and Senate Armed Services Ranking Member James Inhofe, R-Okla., in a joint statement.

Mullah Mohammad Fazl, left, and Abdul Haq Wasiq are shown in these undated photos. Image credit: Department of Defense

"In executing this transfer, the President also clearly violated laws which require him to notify Congress thirty days before any transfer of terrorists from Guantanamo Bay and to explain how the threat posed by such terrorists has been substantially mitigated. Our joy at Sergeant Berghdal's release is tempered by the fact that President Obama chose to ignore the law, not to mention sound policy, to achieve it," they said in the joint statement.

A senior administration official responded: "Due to a near-term opportunity to save Sergeant Bergdahl's life, we moved as quickly as possible. The administration determined that given these unique and exigent circumstances, such a transfer should go forward notwithstanding the notice requirement" of the National Defense Authorization Act, the law in which Congress levied the Guantanamo-transfer restrictions.

The detainees left Guantanamo this afternoon for Qatar, which will take them into custody. After that, it's not clear exactly what their status will be.

Obama said today that he has received "assurances that [Qatar] will put in place measures to protect our national security," and a senior Defense official told ABC that Qatar will be able to secure the detainees. They will also be subject to a travel ban for one year, the Defense official said.

It's not entirely clear what freedom of movement and communication these now-former detainees will enjoy.

The exchange had been discussed previously, and an opportunity to pursue it arose this week, U.S. administration officials said. It was facilitated by Qatar and its emir, Sheikh Tamim bin Hamad Al Thani, with whom Obama said he has spoken.

Obama and Secretary of State John Kerry thanked the Qatari leader in their statements on Bergdahl's release.

ABC's Ali Weinberg contributed to this report.