WASHINGTON—U.S. manufacturing activity picked up in May as pent-up demand amid a reopening economy boosted orders, but unfinished work piled up because of shortages of raw materials and labor. The Institute for Supply Management (ISM) said on Tuesday its index of national factory activity increased to a reading of 61.2 last month from 60.7 in April. A reading above 50 indicates expansion in manufacturing, which accounts for 11.9 percent of the U.S. economy. Economists polled by Reuters had forecast the index rising to 60.9 in May. A shift in demand to goods from services as the COVID-19 pandemic kept Americans at home, strained supply chains, with the virus also disrupting labor at manufacturers and their suppliers, leading to raw material shortages across industries. More than half of adults in the United States are now fully vaccinated against COVID-19, allowing authorities to lift pandemic-related restrictions on businesses. That is whipping up …