Explosions and fire ripped through an infamous toxic waste dump at Elizabeth, N.J., yesterday, sending drums of chemicals flying through the air and spewing black smoke over a 15-mile radius. Five firemen were hurt, none seriously.

Schools on Staten Island and in Elizabeth were closed and residents were warned to avoid breathing the smoke from the Chemical Control Corp. site, even though iniitial tests found the smoke to be "not particularly dangerous," according to the Environmental Protection Agency.

Officials chorused their relief that 10,000 drums of the worst chemicals had been removed from the site over the past year and that the weather had cooperated, blowing most of the smoke out to sea. The fire, which began around midnight, was brought under control by midmorning, although it continued to burn.

The 3 1/2-acre dump had been repeatedly cited as an example of the nation's toxic waste disposal problem. The EPA had planned to use it as the site next week for a press extravaganza announcing new disposal regulations that would help control such abuses.

When New Jersey shut the company down in January 1973, if found 35,000 to 40,000 rusting, punctured 55-gallon drums stacked five deep inside and outside several buildings, right to the ede of the Elizabeth River. Extensive legal proceedings were needed to give the state full cleanup authority, but emergency operations removed 10,000 barrels of the worst stuff: nerve gas, cyanide, PCB's, nitric acid.

"We were very lucky," said EPA spokesman Frank Nepal in New York. "If this happened a year ago it would have been a lot worse."

He said a smoke test taken by helicopter yesterday morning found less than one part per million in the air of benzene, toluene, xylene and ethylene dichloride, concentrations he said were "not particularly dangerous."

New York Mayor Edward Koch visited the scene early yesterday and said precautionary warnings were issued to recognize a danger level similar to "a smog alert in California."

The cause of the fire, which began near an old incinerator on the site, was not known.