Bowing to pressure from both the gun lobby and the Reagan administration, the House yesterday cut $5 million from the proposed $155.6 million budget of the Bureau of Alcohol, Tobacco and Fire-arms.

The 279-to-141 vote on the amendment to the Treasury Department's fiscal 1982 funding bill came after fier speeches by Rep. John Ashbrook (R-Ohio) and James Weaver (D-Ore.), citing the bureau's abuses against gun owners. Cutting its budget would send the bureau "a clear message to stop the intimidation of the average American," Ashbrook said, adding that he could fill 500 pages with specific incidents of harassment.

Rep. Mario Biaggi (D-N.Y.) a former policeman, called the amendment "non-sense," citing the nation's "meteoric rise in crime" and the bureau's role in investigating arson, the bombing of synagogues and the infiltration of organized crime into the liquor industry. The bureau, he said, helps local police departments by making 60,000 traces of firearms a year.

Rep. Delbert Latta (R-Ohio), the amendment's sponsor, argued that he was merely cutting the bureau down to the amount requested by the administration. Although the entire $9.1 billion bill, which includes the postal service, White House offices and several independent agencies, as well as Treasury, is $99 million less than the president's request, the administration has been trying to force Congress to adhere to Reagan's budget proposals line by line.

Other amendments are expected to be debated Thursday, when the House again takes up the bill.