There will be no 4 or 5 train service at Borough Hall, or anywhere in Brooklyn, or in Manhattan below the Brooklyn Bridge/Chambers Street station, from midnight tonight (Friday) until 5:00 a.m. Monday. None, nada, zilch. If you want to go to the East Side of Manhattan, the MTA advises you to take the 2 or 3 to Atlantic Avenue and change there to the J shuttle, running on the Q line, which will take you to Brooklyn Bridge/Chambers Street, where you can get an uptown 4 (there is no 5 service at all) for points north. Got that?
Brooklyn-bound R trains will be re-routed over the Manhattan Bridge, so there will be no service at Court Street in that direction. You can ride the train over the bridge to Atlantic Avenue and transfer to a Manhattan-bound 2 or 3 to Borough Hall or Clark Street, or, to get here from Manhattan, you can use the 2, 3, A, C, or F, all of which will be running normally, except that the Brooklyn-bound A and C will be skipping the 50th Street, 23rd Street, and Spring Street stations. The Manhattan-bound R will be running normally and stopping at Court Street, so it can be used as an option to the 4 or 5 for lower Manhattan stops.
