Housing starts crashed 10.7 percent last month to an annual rate of 937,000, their lowest level for more than five years, the Commerce Department reported yesterday. High interest rates have hit the industry, which is one of those most sensitive to rate movements.

Meanwhile, personal income rose by 1.1 percent in August, with a quarter of the gain due to higher interest income, another Commerce Department report said yesterday. This illustrates that although some sectors are very badly affected by sustained high interest rates, others are benefiting.

People apparently dipped into their savings to increase personal spending by 1.4 percent last month, the report showed. The $26.9 billion annual rate rise in incomes and $27.1 billion increase in outlays were taken by some analysts as further evidence that the overall economy is holding up reasonably well in the face of sky-high interest rates.

Many experts have predicted that the economy will slide under the impact of high rates, but so far the declines have been only small. The housing and auto industries, which depend more than most on the availability of cheap credit, have borne the brunt of the slowdown.

Factory capacity utilization slipped 0.6 of a percentage point in August to 79.2 percent, according to another report from the Federal Reserve yesterday. Declining auto production was the biggest factor in the overall decrease. Figures released earlier in the week had shown a fall in auto output last month and an overall drop in industrial production of 0.4 percent.

Housing industry spokesmen reacted strongly yesterday to news of the August drop in housing starts. "It's a terrible, terrible number," said economist Michel Sumichrast of the National Association of Home Builders. "We are being killed by high interest rates."

The executive vice president of the Mortgage Bankers Association of America, Mark J. Riedy, commented that the figures "have simply caught up with reality and verify what we have been saying all along: that the housing industry is in worse shape than at any time since the mid-1970s."

He criticized the Reagan administration for excessive federal deficits that are making money policy "too restrictive, perhaps of necessity." Housing starts for single-family homes were the lowest ever at 591,000 on an annual basis, the Home Builders Association said.

Building permits for August also were authorized at a low, seasonally adjusted annual rate of 863,000 units, 36 percent below the rate in August last year. Unless mortgage interest rates fall to about 15 percent by the middle of next year, 1982 will be as bad for housing as 1981, Sumichrast said.

The separate Commerce Department report on incomes and spending showed that wages and salaries rose by $16.2 billion last month, up from a $10.7 billion increase in July. Total personal incomes did not climb as much in August as in the previous month, largely because the July number was inflated by a cost-of-living increase for Social Security recipients.

Commerce Department economist Theodore Torda cautioned that the strength of consumer spending last month depended heavily on a surge in car sales, encouraged by special and temporary promotions that cut profit margins. Without this, spending would have been "pretty dreary," he said.

The latest figure for personal saving showed a drop of more than 5 percent in total savings in August to an annual rate of $108 billion. The saving rate -- proportion of net income which is saved -- slipped from 5 1/2 percent in June to 5.4 percent in July, the Commerce Department report said.