The Commerce Department reported that orders fell 0.5 percent, pulled down by falling demand for military and transportation equipment. That followed increases of 0.8 percent in April, 1.5 percent in March and 1.7 percent in February.
Excluding military hardware, factory orders rose 0.2 percent in May from April. Orders for transportation equipment fell 2.9 percent. Orders for computers and electronic equipment fell 2 percent, biggest monthly drop since December.
Orders for durable goods, meant to last three years or more, fell 0.9 percent in May. Orders for nondurable goods slipped 0.2 percent.
Factory orders were up 2.5 percent from May 2013.
U.S. factories have been busy. The Institute for Supply Management reported Tuesday that manufacturing expanded in June for the 13th straight month, though the pace of growth slowed from May.
A measure of employment showed that factories added jobs for the 12th straight month; the pace of hiring last month was the same as in May.
Manufacturers added 10,000 jobs in May as overall U.S. employers created more than 200,000 jobs for the fourth straight month, longest such stretch since 1999. The government's employment report for June comes out Thursday.
The U.S. economy shrank at a 2.9 percent annual rate from January through March. But economists blame the first-quarter drop on an unusually bitter winter and a sharp reduction in businesses' inventories. They expect economic growth to rebound to an annual pace of 3 percent or more the rest of the year, boosted by rising consumer demand and a rebound in U.S. export sales.
Economists have been worried about the fallout from slower economic growth in China. But a survey out Tuesday showed that Chinese manufacturing grew in June for the first time in six months, though the expansion was weak. HSBC Corp. said Tuesday its purchasing managers index for China rose to 50.7 from May's 49.4 on a 100-point scale. Numbers above 50 signal growth.