It is clear that Union infantry and cavalry engaged the rioters in the streets, contributing to the substantial loss of life:
During the Draft Riots of 1863, Union troops were called in to restore order. Here the rioters (pictured) battled Union forces along First Avenue, between 11th and 14th Streets (note the cannon firing in the background) Columbia University, courtesy of New York Public Library
It is also true that cannons - some on land, some on naval vessels - were deployed. The artillery on land was indeed used, but it is unclear whether there was also a bombardment from sea.
Today, Gramercy Park is a quiet place, but in 1863 it was a war zone. Union cavalry and artillery occupied the park, setting up two cannon at the northeast corner to face the rioters.
- Columbia University
When detectives heard rumors of a looming attack upon the Treasury vaults on Wall Street, two warships were dispatched from the Brooklyn Naval Yard, their cannon covering the lower end of Manhattan.
- Cleveland Civil War Roundtable
By the fourth day, NYC resorted to extreme measures by firing cannons at the angry mobs. By the evening, more than 4000 trained troops were fighting to control the violent mobs. Finally, by the next morning, the rioters were subdued.
- Baruch College
The quotes above say that battleships from the Brooklyn Navy Yard were sent out to cover lower Manhattan because of a rumored threat to the gold vaults on Wall Street, while the cavalry and infantry cannons were deployed to Gramercy Park.
Here we see that Wall Street is just south of Five Points, Gramercy Park is well north of Five Points. It would make sense for the naval artillery to be aimed around Five Points, but that doesn't mean that those cannons actually came into play.
The only source I've found that mentions a naval bombardment of the Five Points doesn't offer any citations, and therefor, must be taken with a grain of salt.
More than ten thousand soldiers from the Army of the Potomac, who had just finished chasing Lee’s Army back to Virginia, arrived in New York furious. Enraged to have defeated an army of secessionists only to find rebellion in their backyard, the soldiers were not delicate with rioters. Using rifles, artillery, cavalry and naval bombardment the Army battered the mob back into Five Points killing, maiming and wounding as it went.
- History Revived
More sources claim that the Navy did not engage:
Although the naval bombardment depicted in the recent film Gangs of New York did not occur, federal troops used artillery against the rioters, who numbered in the thousands.
- Sage American History
There was no crazy fight like Martin Scorsesse portrays, with gangs murdering 100s and the U.S. Navy bombarding New York City.
- Mike the History Guy
Troops and ships were deployed, artillery was fired, but I haven't been able to find a credible source that confirms a naval bombardment of the city. It seems to be possible, but far from certain, and it probably didn't happen.