Question: What is the name of the historic hay and livestock barn located in a hamlet in Suffolk County with a population of 5,945 as per 2010 census?

Context paragraphs:
Center Moriches, New York: Center Moriches ( ) is a hamlet (and census-designated place) in Suffolk County, New York, United States.  The population was 7,580 at the 2010 census.  Center Moriches is in the town of Brookhaven.  It is the location of the historic Masury Estate Ballroom and Terry-Ketcham Inn, both listed on the National Register of Historic Places.

North Bay Shore, New York: North Bay Shore is an unincorporated neighborhood on Long Island in the Town of Islip in Suffolk County, New York, United States.  The area is a suburb of New York City.  The hamlet of "North Bay Shore" is within the northern part of the CDP of Bay Shore, New York.  The census-designated place (CDP) named "North Bay Shore" is north of, and adjacent to, the hamlet named North Bay Shore.  The CDP of North Bay Shore contains the hamlet of Pine Aire and part of the hamlet of Brentwood.  The population of the North Bay Shore CDP was 18,944 at the time of the 2010 census.

Rowe Farm: Rowe Farm is a historic home and farm located near South Bethlehem, Albany County, New York.  The farmhouse was built about 1875, and is a two-story, Italianate style frame dwelling with a gable roof.  It has a center hall plan and a gable roof.  Also on the property are the contributing Main Barn / Hay Barn (c. 1879), out kitchen (c. 1800), smokehouse (c. 1875), livestock barn (c. 1790), ice house, shed and outhouse, pig barn, carriage barn (c. 1875), shed, fowl house, and blacksmith shop.

Miller Place, New York: Miller Place is a hamlet and census-designated place (CDP) in Suffolk County, New York, United States, on the North Shore of Long Island.  Miller Place has been inhabited since the 17th century and is named for the Miller family that included many of its initial settlers.  For most of its history, the community functioned as an agriculture-based society.  Despite preserving much of its historic identity, changes in the 20th century have transitioned the hamlet into a desirable and densely populated suburban area.  The population was 12,339 at the 2010 census.

Suffolk County Almshouse Barn: Suffolk County Almshouse Barn is a historic hay and livestock barn located at Yaphank in Suffolk County, New York.  It was built in 1871 and the large multi-story barn has a broad gable roof and wood shingle sheathing.  It is the only extant structure from the Suffolk County Almshouse.

Blunt House Livestock Barn: The Blunt House Livestock Barn is a historic barn in rural White County, Arkansas.  It is located on the north side of County Road 94 (Babb Road), west of the hamlet of Midway.  It is a wood frame structure 1-1/2 stories in height, with a gambrel roof and a shed-roof ha storage extension to the east.  It is finished in board-and-batten siding; its roof is corrugated metal.  Built c. 1920, it is the county's best example of barns built between about 1914 and 1939.  The barn is somewhat rare, as gambrel roofs were not commonly used in barn construction in the county before 1930.

Huntington, New York: The Town of Huntington is one of ten towns in Suffolk County, New York, United States.  Founded in 1653, it is located on the north shore of Long Island in northwestern Suffolk County, with Long Island Sound to its north and Nassau County adjacent to the west.  Huntington is part of the New York metropolitan area.  As of the United States 2010 Census, the town population was 203,264.

Yaphank, New York: Yaphank ( ) is a hamlet and census-designated place (CDP) in Suffolk County, New York, United States.  The population was 5,945 at the time of the 2010 census.

Mount Sinai, New York: Mount Sinai is a hamlet and census-designated place (CDP) located within the Town of Brookhaven in Suffolk County, New York, United States.  The population was 12,118 at the 2010 census.  The hamlet is located on the North Shore of Long Island, and is served by the Mount Sinai School District and the Mount Sinai Fire Department, founded on October 25, 1930.  The Mount Sinai Fire District covers approximately 5.5 square miles including the Mount Sinai Harbor and parts of the Long Island Sound.  Mount Sinai's ZIP code is 11766.

Riverhead (town), New York: Riverhead is a town within Suffolk County, New York, on the north shore of Long Island.  As of the 2010 census, the population was 33,506.  The town rests on the mouth of the Peconic River, from which it derives its name.  Since 1727, Riverhead has been the county seat of Suffolk County.  The smaller hamlet of Riverhead lies within it, and is the town's principal economic center.  The town is 166 miles (267 km) southwest of Boston via the Orient Point-New London Ferry, and is 76 miles (123 km) northeast of New York City.

Supporting paragraphs: Suffolk County Almshouse Barn Yaphank, New York
Answer: Suffolk County Almshouse Barn