The administration yesterday announced its support for a $5 billion federal line of credit to prop up the failing Farm Credit System on condition that the nation's largest agricultural lender streamline its management practices.

Another and possibly more controversial element of the administration plan would provide more capitalization by transferring to the credit system at least 500,000 acres of government-owned farm land from the Farmers Home Administration (FmHA) "surplus" inventory.

Charles O. Sethness, an assistant treasury secretary, told a House subcommittee that the administration agreed the system faces "potential disaster" but that management reforms should be achieved and system reserves spent before federal aid becomes necessary.

"The current overlapping, overlayered, overprotected system breeds waste and bad management," Sethness said. "We cannot afford the costs this imposes on farmers, borrower-stockholders and now, potentially, the taxpayer."

"We cannot afford to make billions of dollars available without sound incentives, informed and effective controls and a concept of how to improve the underlying problems."

Officials of the system, which holds about one-third of the nation's farm debt, have urged Congress to approve a $6 billion line of credit this year to avert a collapse. Falling land values, increasing bad debts and declining loan volume have caused system losses of $4.6 billion in the last two years, with an additional $1 billion loss looming this year.

The three directors of the Farm Credit Administration, the quasi-federal regulator of the system, agreed that the farmer-owned lending network must have government help to survive, but they differed on how to force the system to improve its management practices.

Frank W. Naylor Jr., chairman of the Farm Credit Administration board, noted that the system still had capital of $5.2 billion, including a $1.2 billion surplus, that has not been used "in the self-help process anticipated by Congress" with legislation that opened the way for federal aid.

Under the 1985 law, the system was required to commit its resources to self-help measures before it could obtain federal funds. Transfer of funds from healthy districts to troubled districts has been stymied by litigation.

Naylor also said that the system must change some operating procedures and cut its $800 million annual overhead "if it is to remain an active participant in the financial services industry." He said the system should be forced to end staff duplication and unnecessary labor on low-yield loans and close unproductive offices to cut costs.

But director Jim Billington argued that the system had met the 1985 requirements for federal assistance and warned that "if the system doesn't receive funds soon, the weakest federal land banks will pull the entire FLB system down."

The land banks, a part of the lending network, have been hit hard by a 30 percent drop in performing loans and a 21 percent drop in total loan volume since March 1986, while interest income is down 25 percent and acquired property has increased 21 percent, Billington said.