The government provided new evidence yesterday that the economy is continuing to slide: Retail sales plunged further in May, while business served notice it is beginning to scale back its capital spending plans.

In companion reports, the department said sales levels fell a sharp 1.5 percent in May following a revised 2.3 percent plunge in April, marking the fourth month in a row that retail sales have declined.

At the same time, a new department survey in Late April and May shows business have begun to cut back on investment in new plant and equipment -- a trend that could prolong the recession if the the belt-tightening continues.

The survey shows firms now intend to boost their capital spending by only a slim 1 percent this year, after adjustment for inflation -- down visibly from a 2.6 percent rise projected three months before.

William A. Cox, the department's deputy chief economist, cautioned that the capital-spending figures still weren't conclusive. He said the findings show "some scaling-back, but certainly no collapse."

Nevertheless, taken together, the reports added to other indications that the economy still is sliding. Most economist expect the recession to continue through the remainder of this year, followed by a weak recovery.

There was some glimmer of hope in yesterday's sales figures: The May decline clearly was not as steep as April's. And three-quarters of it was centered in auto sales. Nonauto sales edged down only 0.5 percent.

Since the recession began last January, overall retail sales levels have plunged 7.3 percent, but the decline for the most part has been concentrated in the auto industry.

Departmental figures show auto sales have plummeted some 27 percent so far this year, while sales outside the auto industry have dropped a more modest 2.4 percent. However, the decline has become more pervasive in recent months.

Yesterday's figures showed overall retail sales levels in May at a seasonally adjusted $73.66 billion, down from $74.77 billion in April. The department earlier had estimated the April decline at 1.2 percent.

Sales of durable goods fell 4.3 percent in May to a seasonally adjusted $21.72 billion, following a 6.6 percent drop in April. Nondurables sales dipped 0.3 percents to $51.94 billion.

Even with the past several months' declines, total retail sales still were up to 1.9 percent from their levels of a year ago. Sales of durable goods were down 14.2 percent from May 1979, but nondurables were up to 10.6 percent. w

Along with the decline in auto sales, the next-biggest drop over the year was posted by construction materials, whose sales levels fell by 13 percent from May 1979. Retail gasoline sales soared 31 percent, mainly from price hikes.

The survey on business spending plans showed investment in new plant and equipment likely to rise 9.9 percent this year. However prices of capital goods have been rising at an 8.5 percent annual rate.

Business investment in new plant and equipment rose 6 percent after adjustment for inflation in 1979. Actual spending on capital goods in the first quarter of this year was about 1 percent higher than plans reported in March.