In relative population terms it's like saying there wasn't a single shooting in Louisiana and Mississippi for 5 days. Those two states have a combined population slightly smaller than NYC but have the highest rates of gun violence in the country.
They are also poorer than NYC and much more spread out, so enforcing the law is somewhat harder. Also, if you plotted out "shootings per gun" and "self-defense incidents involving a gun" I'm sure you would find it's not as bad as you think. Guns in the hands of normal people prevent crime.
Population density is often cited as a reason for higher rates of gun violence. I'm not sure about you "spread out" theory of law enforcement. Those are not the most "spread out" states in the country, nor are they the states with the highest levels of self-defense associated gun violence.
If you read the story, the incident that broke the 5 day streak in NY was an individual attempting to stop a hit and run driver that had crashed into a neighbors parked car.
That's not exactly what I was trying to say. All crime is more prevalent in NYC, and it is one of the hardest places to legally purchase a gun. So criminals who disregard the law can have guns and normal people can't, effectively. The laws are such that if you use a gun in self-defense, you are very likely to be charged with murder. The few gun crimes that do happen in NYC are committed by criminals who would have likely been violent anyway.
Big cities have more crime per capita for whatever reasons, perhaps because of their laws. There are generally more police per capita as population increases. See this for example: https://www.governing.com/archive/police-officers-per-capita...
Depriving people of guns is not a reasonable answer to gun crime, any more than depriving people of knives because of knife crime or cars because of car crime. Gun crime is unfortunate, but so is getting jumped by 5 dudes, robbed in your home or business, or gang-raped because you have no way to defend yourself. No amount of police will save you from that. The police also won't save you from government tyranny.