The Republican-controlled Senate Banking Committee broke with the White House yesterday and approved a $5 billion bill to bail out the ailing housing industry by subsidizing mortgage interest rates for buyers of new homes.

The committee sent the bill to the Senate floor by a vote of 15 to 1 after rejecting amendments by Democrats to provide the assistance in sales of existing homes as well and make it available to as many people in high as in lower income areas. The committee also refused to add a loan program to help newly unemployed homeowners avoid mortgage foreclosures.

The housing industry, which supported President Reagan in the 1980 election and up to now has backed his economic program, has been devastated by the high interest rates of recent months and is clamoring for special help from Congress.

But the administration has said it cannot support the bailout bill, introduced by Senate housing subcommittee Chairman Richard G. Lugar (R-Ind.), because of its cost. Sponsors say, however, that any costs in the $1 billion-a-year, five-year program will be temporary, because the benefiting buyers will have to repay the interest subsidies when they sell or refinance their homes.

No action has been taken on a housing bill in the House, where the controlling Democrats have a costlier plan that would also increase housing aid to the poor.

Under the interest "buy-down" plan, the federal government would subsidize up to 4 percentage points of mortgage interest rates. At today's Federal Housing Administration rate of 15 1/2 percent, this would mean eligible home buyers would pay an 11 1/2 percent rate for the five-year duration of the program.

After that the rate would escalate to whatever the original FHA rate was as long as the family continued to hold the mortgage.

The interest-rate subsidy could be worth as much as $13,245 to a home buyer over the five-year period, but this would have to be paid back to the government whenever the home was resold or refinanced.

The sponsors are hoping that interest rates will decline within the next five years to a point where most people would want to refinance, and the government would get its money back quickly.

The legislation generally is limited to persons with incomes of up to $30,000 a year and a new mortgage of $67,500.

The panel amended this, however, to give the Department of Housing and Urban Development discretion to raise these limits to $37,000 in income and $77,625 in mortgages in high-cost locations, such as the Washington area.

Moderate-income people who in the past could afford to buy homes in this range--and qualify for mortgages on them--in recent years have been unable to purchase because high interest rates have made monthly payments skyrocket.

High interest rates are generally regarded as the main culprit in the housing industry's current problems.

The total purchase price of a home bought under the program is not limited, but the subsidy would be available only on homes built after April 1 of this year.

The idea behind the restriction is to stimulate new construction and jobs.

Senate Banking Chairman Jake Garn (R-Utah) said Congress must act within the next month on the legislation for it to have the desired impact on home building and jobs during this building season, and he said he would ask the Senate leadership to speed its consideration.

Sen. William Proxmire (D-Wis.) yesterday expressed the most doubt about the program and its impact, but supported the bill anyway.

"I feel that it is just intolerable of us to allow the home building industry to be in the state it's in" with large numbers of builders failing through no fault of their own, Proxmire said. "Rather than hunker down and wait until something turns up, we have to take some action."

The lone dissenting vote was cast by proxy for Sen. William L. Armstrong (R-Colo.).