Retail sales jumped by 1.5 percent last month after a revised April increase of 0.7 percent, the Commerce Department reported yesterday, adding to the indications that the economy is gradually beginning to turn around.

The May increase was stronger than analyts had expected, but the April sales figure had to be revised downward because of additional data. The Commerce Department originally estimated that retail sales rose 1.4 percent in April.

Nevertheless, Commerce Department Chief Economist Robert Ortner said yesterday's release was "very encouraging." The consecutive increases in sales in April and May were "impressive." agreed Allen Sinai of Data Resources Inc. Sinai added that, while the retail report was not enough on its own to signal the end of the recession, "it's one of those scattered signs that we will be getting in coming months" that the economy is beginning to turn around.

Unemployment will still continue to rise in coming months, however Sinai said. The business sector is still extremely weak and, despite the resilience inthe consumer sector, the jobless rate is likely to climb to the "upper 9s," Sinai commented. In May the unemployment rate was 9.5 percent.

Initial claims for unemployment insurance rose to 619,000 in the week ending May 29, the Labor Department reported yesterday. This level has only been exceeded twice before in this recession, and yesterday's release suggests that the job market is still deteriorating.

The retail sector is "one sector that continues to show encouraging figures," Ortner said. He remarked that if there is to be an economic recovery, the coonsumer will have to "accomplish it...Housing will not lead the way, nor will capital investment." Earlier, the Commerce Department had released figures showing a sharp drop in business plans for new capital spending this year.

Sinai said that the economy "was within a month or two of the trough" of recession.

Treasury Secretary Donald T. Regan also said yesterday that the recovery would likely be "conumer oriented." He toold reporters at a breakfast meeting that if Congress agrees to a budget along Republican lines, the economy should grow by between 4 percent and 4 1/2 percent in the second half of the year. With out a budget compromise, he warned, growth will be only half as fast.

Regan compared a recession to an earthquake, saying that after an earthquake "the weakest building always shows the cracks first, and indeed some of them collapse." Business bankruptcies have been rising rapidly this year.

Big ticket items, particularly autos, improved last month. There was a 2.5 percent increase during May in sales of durable goods, such as washing machines, autos and other long-lasting consumer products, the report said. There had been an even bigger increase of 3 percent in the previous month.

The recession, however, hit hard at durable goods sales earlier in the year, so that, despite their recent strength, durable goods sales were only 3.5 percent higher last month that they had been in May 1981.

If auto sales are excluded, sales of other retail goods were up by only 1 percent in May, yesterday's report said. That compares wiith a slide of 0.2 percent between March and April.

Auto sales climbed by 4 percent in May, the report said, after a 5 percent increase in April. Car sales have been boosted by rebates and special financing deals and may fall of when they end, as interest rates have stayed high.

General merchandise stores, including department stores, also boosted sales by 4 percent. The figures are seasonally adjusted, but do not take account of price changes.