The economy is growing at a 5% percent annual rate this quarter, according to preliminary unpublished estimates by the Commerce Department.

This so-called flash estimate made before the quarter ends to assist administration officials shows considerably stronger growth than most forecasters have been expecting.

However, most forecasters believe that slowing consumer spending, business investment and residential construction will produce a downturn in the second quarter and perhaps in the third as well.

The Commerce Department, in a published report, yesterday revised downward for the second time its estimate of how fast the economy grew in the last quarter of 1980. After adjustment for inflation, output was first estimated to have risen at a 5 percent annual rate in the quarter. That estimate then was revised downward to a 4 percent rate, and yesterday was lowered to a 3.8 percent rate.

Corporate profits after taxes rose $5 billion in the fourth quarter of 1980 to a seasonally adjusted annual rate of $164.1 billion, but were still well below the $182.9 billion rate reached in the first three months of the year, the department said.

Separately, the Federal Reserve Board said the nation's factories used only 79.3 percent of their productive capacity in February, a 0.7 percent drop from the previous month. The capacity utilization rate for industrial materials producers fell half a point to 81.2 percent.

The operating rate for manufacturers of motor vehicles and parts declined moderately, the Fed reported, reaching a very low 57 percent of capacity. Nevertheless, Commerce Department analyst Ken Patrick said unpublished figures for the industry indicate that while it still lost money in the quarter, it lost much less than in the previous three months. Auto industry profits fell at a $9 billion annual rate in the second quarter and at a $5 billion rate in the third.

The drop in capacity utilization throughout the economy in February had been expected in light of the 0.5 percent drop in industrial production reported by the Fed on Tuesday. Despite the indications that the economy is slowing, Federal Reserve Governor Lyle Gramley told the Boston Economic Club that a recession is unlikely this year.

"Following a lull in the second quarter, the pace of economic growth will pick up again [in] the second half," Gramley said.

One reason the economy has continued to expand so far this year was that in the previous quarter, sales of goods to consumers and business outpaced production, causing a decline in inventories. So-called final sales, after adjustment for inflation, rose at a 4.4 percent annual rate in the quarter, according to the Commerce report. The level of business inventories fell somewhat more rapidly than in the previous quarter. A low level of inventories relative to sales usually leads to new orders for replacement goods.

At a $164.8 billion annual rate, corporate profits in the fourth quarter were running slightly below their level for all of 1979 when they reached $167.8 billion. Ken Goldstein, a spokesman for the Conference Board, termed the increases in the quarter "very, very small." The figures indicate business in general has "not recovered in terms of profitability, as opposed to profits," with margins still lower than they were before the 1980 recession, he said.

Meanwhile, there were signs that a further decline in the prime rate could be imminent. Two major banks slashed their broker loan rates by half a percentage point, with Irving Trust, the nation's 14th largest bank, lowering the rate charged on loans to brokers with stock as collateral to 15 1/2 percent from 16 percent.

In an earlier move, Continental Illinois National Bank & Trust Co., the nation's seventh largest, lowered its broker rate to 15 3/4 percent.

On Tuesday, most of the nation's major banks lowered their prime lending rate to 17 1/2 percent from 18 percent. Changes in the broker loan rate often precede movements in the prime rate that banks charge their most credit-worthy corporate customers for short-term loans.