The engine of Southwest Airlines Flight 1380 failed on Tuesday about 20 minutes into its flight from New York City to Dallas. Debris from the engine blew out a window causing the woman, Jennifer Riordan, to almost get sucked out of the plane.
Passengers dragged Riordan back into the cabin but she died at a Philadelphia hospital after the plane made an emergency landing.
In a letter to passengers on Thursday, the airline expressed "sincere apologies" for the fatal incident and included the cheque, said Kamau Siwatu, who was aboard the flight, CNN reported.
He was one of the passengers who said they received the letter. "We value you as our customer and hope you will allow us another opportunity to restore your confidence in Southwest," the letter addressed to Siwatu stated.
"In this spirit, we are sending you a cheque in the amount of $5,000 to cover any of your immediate financial needs."
In addition to the money, passengers will also receive a $1,000 travel voucher, the letter said.
The plane's engine had undergone a visual inspection two days before, the airline said. The National Transportation Safety Board (NTSB) was finishing up its initial examination into the engine failure -- but many questions remained unanswered.
It was unclear why the left engine of the flight malfunctioned when the plane was over 32,000 feet.
Federal officials recovered the airplane's cockpit voice recorder and flight data recorder. They were still tracking down debris from the engine.
The NTSB will look into how an interior crack on a fan blade led to the engine failure. NTSB chairman Robert Sumwalt said the crack was not detectable from the outside. One of the cracks was consistent with metal fatigue, he said.
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