The strike is likely to add to the airline's economic woes, after it suffered reduced demand during the global economic downturn and lost revenue again when a volcanic ash cloud from Iceland disrupted travel over Europe for more than a week in April.
The company posted a pre-tax loss of $765m last week, the largest annual loss since the airline was privatised in 1987.
Sales are slumping and company officials say they need to extract 90m in concessions from workers in order to stay competitive.
Barbara Serra, Al Jazeera's correspondent at Heathrow airport, said: "British Airways planes have been landing and taking off at Heathrow airport on day one of [the] strike.
"But around half of scheduled flights have been grounded due to the longstanding dispute over working conditions and perks.
"BA say they can fly 60,000 booked passengers every day of this strike and can arrange for throusands more to reach their destinations by booking them on other airlines.
"But these contingency plans are costly and temporary. What is needed is for the union and the airline to come to some agreement, but they remain poles apart."
Unite, the union representing cabin crews, and the company have reached agreements in principle over pay rates.
But stumbling blocks in the negotiations include disagreements over perks, such as staff travel concessions.
The union also wants immunity for more than 55 of its members who were sacked or face disciplinary action for their involvement in the dispute.
On Saturday, Willie Walsh, BA's chief executive, had to be taken out of negotiations under police escort, after protesters from the far-left Socialist Workers Party stormed the building where negotiations were taking place.
The protesters learned about the meeting's location after Derek Simpson, co-leader of the Unite union, posted information about the negotiations on the social networking site Twitter.
BA criticised the union for posting the location, saying that such a move damaged trust in the negotiations.
Tony Woodley, joint leader of Unite, was seen screaming "shut up" at the protestors.
He later said the dispute turned personal because he believes the airline dislikes the cabin crew union.
In addition to the current strike, BA staff are planning two further five-day strikes beginning on May 30 and June 5.