"Five Points" was the intersection of five streets: Mulberry Street, Anthony (now Worth) Street, Cross (now Park) Street, Orange (now Baxter) Street, and Little Water Street (no longer existing). The former "Five Points" area is now part of Chinatown and is also partly covered by court buildings.
Wikipedia: Five Points, Manhattan
Five Points (or The Five Points) was a neighborhood in lower Manhattan, New York City, New York. The neighborhood was generally defined as being bound by Centre Street in the west, the Bowery in the east, Canal Street in the north and Park Row in the south. The former Five Points is now split between the Civic Center on the west and south and Chinatown on the east and north.
Five Points gained international notoriety as a disease-ridden, crime-infested slum that existed for well over 70 years.
"Five Points" was derived from the five-pointed intersection created by Orange Street (now Baxter Street) and Cross Street (now Mosco Street); from this intersection Anthony Street (now Worth Street) began and ran in a northwest direction, dividing one of the four corners into two triangular-shaped blocks; thus the fifth "point". To the west of this "point" ran Little Water Street (which no longer exists) north to south, creating a triangular plot which would become known as Paradise Square after the buildings standing in the triangle were torn down in 1832.
25 August 1826, New-York (NY) American. "Police-Office," pg. 1, col. 2:
It is probably very well known that that is a district, lying between Broadway and the Bowery, comprising Anthony-street, Collect-street, Orange-st., and the Five points, which goes under the general name of The Collect.
14 February 1827, The National Advocate (New York, NY), "A couple of Gentlemen," pg. 2, col. 4:
Two gentlemen were brought before the magistrate this morning, having laid all night in the watch house, charged with assault and battery on a black man, at a place called the Five Points.
23 December 1828, New-Hampshire Gazette, pg. 2:
Murder and Suicide. - Joseph Dougherty, keeper of a house of ill-fame, at the Five Points, a sink of iniquity in the city of New-York, on Tuesday last stabbed an abandoned women who lived with him as his wife, and who had gone with another man on the day previous.
24 April 1830, Saturday Evening Post, pg. 2:
The Grand Jury of New-York presented, as nuisances, twenty-nine houses in that part of the city called the Five Points, which they described as the abode of "unbounded iniquity."
1 October 1830, The Euterpeiad: an Album of Music, Poetry & Prose, pg. 95:
THE BOWERY THEATRE.
To advert to comic authorship, or rather collation, as displayed in the "FIVE POINTS:" In the local manners of the States on the sea board, with the exception of Yankeeism, there is, it would appear to us, a scantiness of the raw material. - What distinctive character of manners is there to be found, for example, in the low life of New-York?
31 May 1831, New-Hampshire Gazette, pg. 2:
John Harrington has been arrested in New-York, for killing his wife at the Five Points, by cruelly beating her.