The unemployment rate jumped from 7.3 to 7.6 percent last month, but inflation eased markedly as energy prices declined, the Bureau of Labor Statics reported yesterday.

Producer prices rose by slightly less than 0.4 percent in May, equivalent to an annual inflation rate of 4.6 percent. This was half the increase recorded in April, and left the index 10.5 percent above a year earlier. An administration official welcomed the May figures, which he said "suggests that price trends are developing favorably in the near term."

Falling gasoline and heating oil prices were a major factor in last month's improvement. But prices of consumer goods generally rose at a slower rate than in previous months.

This, and the increase in unemployment, are indications that the economy may be slowing down, after having grown faster than predicted in the first quarter. BLS Commissioner Janet Norwood, in testimony before Congress' Joint Economic Committee, pointed especially to a 0.5 percent increase in the normally stable unemployment rate for men, to 6.3 percent, which she said was an indication that basic industries are not producing to capacity.

Deputy White House press secretary Larry Speakes said the increase in unemployment was evidence of the need for President Reagan's economic program, which is supposed to stimulate the economy but not add to inflation.

Private and public economists alike are predicting a softer economy in the second and third quarters of this year, after the growth in the first three months. High interest rates have been one factor braking the economy, analysts say.

The jobless rate had been stable at about 73 percent for the five months to April. Last month's increase took it back to the 1980 peak, last recorded in October. Unemployment increased among all categories of workers in May; the rate for women went up 0.2 percent to 6.8 percent.

Although the increase for the month was large enough to be called significant, a Labor Department analyst cautioned that too much should not be read into one month's figure. It takes two or three months to determine whether there is a change in trend, she said.

The administration is having some good luck on inflation, exonomists say, as energy prices drop and food prices stay steady. Last month's 0.5 percent decline in the prices of fuels ready to be sold at retail was the first for more than three years. Energy prices spurted earlier this year when the president removed federal price controls from oil.

Consumer food prices at the wholesale level have stayed unchanged for two months in a row, and have moved very little in the last six months. Other consumer goods prices were up by 0.6 percent in May, compared with a 0.9 percent increase in April.

However, auto prices continued to rise quite sharply with an increase in the passenger car price index of 1.2 percent in May, after 1.4 percent in April. Capital equipment prices also rose more than the average at 0.9 percent.

Further good price news is ahead, in that prices for crude materials fell 0.5 percednt last month. Goods at the intermediate stage of production went up on average by 0.5 percent last month, the report showed.

The rise in unemployment came despite a 250,000 increase in the number of people with jobs to 99.2 million in May. The increase in jobs was only half as large as that in April, and was not enough, Norwood said, to provide jobs for the expanding labor force.

Manufacturing industries were running flat, she said, while the number of job seekers in those industries climbed from 7.4 percent to 7.9 percent of the labor force in May. There was also a sizable increase in joblessness among construction workers.

Unemployment hits some groups of workers, and some regions, far harder than others. Teen-age unemployment rose from 19.1 percent to 19.5 percent last month, the proportion of black workers out of a job went from 13.2 percent to 13.6 percent and the jobless rate of Hispanics jumped from 9.1 percent to 10.2 percent, the Labor Department report said.

April unemployment rates in the 10 largest states ranged from 5.3 percent in Texas to 11.3 percent in Michigan, the department reported. Massachusetts and California had rates of 6 percent and 6.5 percent respecitvely, while most of the others hovered around 7 percent or 8 percent.