New York City, which prides itself on leading the nation in various endeavors, gained notoriety again today as the site of the nation's largest cash robbery when at least two armed men punched through a roof of tarpaper and sheet metal and made off with an estimated $5.3 million from the headquarters of an armored-car company in the Bronx.

The theft, which police said bore all the earmarks of an inside job, occurred late Sunday night, and the suspects had about a five-hour head start in escaping, authorities said.

It came four years and a day after the nation's largest robbery--the $5.8 million theft of cash and jewelry from a Luft-hansa Airlines cargo area atKennedy International Airporthere.

Police said company officials, who earlier issued a $1 million estimate of the losses and then raised the figure to $8 million, settled on $5.3 million after a complete audit. Police said the shotgun-toting bandits entered the Sentry Armored Courier Corp., a two-story brick building on a busy street, and disarmed and handcuffed the lone guard, who had been watching television on the second floor.

They used crowbars and wire cutters to break through metal doors and enter the money room, police said.

Apparently familiar with the alarm system, police said, the bandits were able to remove money bags without triggering the alarm. They took the cash, mostly in $50 and $100 bills, to a vehicle they had backed into the garage, loaded it and fled, sometime after midnight, police said.

The theft was discovered shortly before dawn, when the guard was heard shouting, police said. They said the guard was not injured.

The guard told police that the intruders surprised him. Asked if the guard, whom police did not identify, was a suspect, police declined comment.

Police, who have joined the FBI in a manhunt, declined to say whether the getaway car had been identified. They were also unable to offer a detailed description of the perpetrators, who wore gloves and ski masks. Police said the robbers left one bit of evidence, a message scrawled on a dusty mirror. It read: "Robbers were here. Ha Ha."

Police were somewhat befuddled today about how burglars could cut through the roof of a building in a fairly active strip in the Bronx without being observed. Police said the men apparently swung through the two-foot hole on a rope, then aimed security cameras at the ceiling.

The bulk of the money, police said, had been en route from the Federal Reserve Bank to area banks. Authorities said about $1 million of the stolen money was in smaller denominations, apparently Saturday night's receipts from Yonkers Raceway.

Yonkers Vice President Jerry Lawrence said a Sentry armored car picked up the receipts Saturday night, but he refused to say how much cash was transferred.

Police theorized that the robbers filled their vehicle because a large pile of cash was left behind on the garage level.

"You and I could retire on what they left behind," a detective said.

The New York Daily News reported tonight that more than $20 million in cash was left behind.

Police spokesman Fred Elwick said, "It's going to be a hell of a Christmas for somebody."

Two months ago, a Sentry guard was killed and another guard and a bystander wounded when four gunmen stole about $65,000 in checks and cash from an armored car outside a Bronx dairy.

No U.S. robbery approaches the world's largest, the theft of $400 million in negotiable securities and $20 million in gold, foreign exchange and jewels from Germany's Reichsbank in 1945. None of that was recovered, although three men were convicted on conspiracy charges in connection with some of the bonds in Canada in 1979.