"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.
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.