The WPA built traditional infrastructure of the New Deal such as roads, bridges, schools, courthouses, hospitals, sidewalks, waterworks, and post-offices, but also constructed museums, swimming pools, parks, community centers, playgrounds, coliseums, markets, fairgrounds, tennis courts, zoos, botanical gardens, auditoriums, waterfronts, city halls, gyms, and university unions. Most of these are still in use today. The amount of infrastructure projects of the WPA included 40,000 new and 85,000 improved buildings. These new buildings included 5,900 new schools; 9,300 new auditoriums, gyms, and recreational buildings; 1,000 new libraries; 7,000 new dormitories; and 900 new armories. In addition, infrastructure projects included 2,302 stadiums, grandstands, and bleachers; 52 fairgrounds and rodeo grounds; 1,686 parks covering 75,152 acres; 3,185 playgrounds; 3,026 athletic fields; 805 swimming pools; 1,817 handball courts; 10,070 tennis courts; 2,261 horseshoe pits; 1,101 ice-skating areas; 138 outdoor theatres; 254 golf courses; and 65 ski jumps. Total expenditures on WPA projects through June 1941 totaled approximately $11.4 billion—the equivalent of $}} today. Over $4 billion was spent on highway, road, and street projects; more than $1 billion on public buildings, including the iconic Dock Street Theatre in Charleston, the Griffith Observatory in Los Angeles, and Timberline Lodge in Oregons Mount Hood National Forest.
Question: Which type of buildings were more than 5000 for each constructed?
Answer: schools | auditoriums, gyms, and recreational | dormitories