So yeah, this excerpt from wiki is interesting. Follow the [citation] links if you're feeling iffy about it:
BP initially estimated that the wellhead was leaking 1,000 barrels (42,000 US gallons; 160,000 litres) a day.[64] On April 28, the National Oceanic and Atmospheric Administration estimated the leak was likely 5,000 barrels (210,000 US gallons; 790,000 litres) a day, five times larger than initially estimated by BP.[65][66] John Amos, a geologist who has worked as a consultant with oil companies on measuring oil spills, said that figure is the "extremely low end" of their estimates, putting a more realistic figure at 20,000 barrels (840,000 US gallons; 3,200,000 litres) a day.[67] Other sources using satellite imagery have put that number as high as 25,000 barrels (1,100,000 US gallons; 4,000,000 litres) a day.[64][68] Ian MacDonald, an oceanography specialist at Florida State University, estimated that oil might be leaking at that rate and that the oil slick (as of May 2, 2010) might already contain more than 210,000 barrels (8,800,000 US gal).[69] He later estimated the spill to be about 290,000 barrels (12,000,000 US gallons; 46,000,000 litres).[70] Mike Miller of Safety Boss, a fire-fighting company that specializes in oil wells, suggested that the oil spill may become the biggest in history.[66]
According to BP, estimating the flow is very difficult as there is no metering of the flow underwater.[66] The company has refused to allow scientists to perform accurate, independent measurements of the flow.[6] In their permit to drill the well, registered officially with the MMS, BP estimated the worst case flow at 162,000 barrels per day [71][72]. After the accident, before Congress, BP estimated 60,000 barrels (2,500,000 US gallons; 9,500,000 litres) per day if the blowout preventer and other equipment restricting the current flow were removed.[73] Experts contacted by National Public Radio and shown underwater footage of oil and gas gushing out of the broken pipe put the leak rate substantially higher.[74] Timothy Crone, an associate research scientist at the Lamont-Doherty Earth Observatory, used another well-accepted method to calculate fluid flows, estimating "at least 50,000 barrels (2,100,000 US gallons; 7,900,000 litres) a day" leaking from the well. Eugene Chaing, a professor of astrophysics at the University of California, Berkeley, correctly estimated the pipe's diameter at approximately 20 inches (51 centimetres). Using just pencil and paper, he arrived at a figure approximating Crone's findings, stating, "I would peg [the flow] at around 20,000 barrels (840,000 US gallons; 3,200,000 litres) to 100,000 barrels (4,200,000 US gallons; 16,000,000 litres) barrels per day." Chaing also claimed the earlier figure of 5,000 barrels (210,000 US gallons; 790,000 litres) barrels a day is "almost certainly incorrect." [75]
Steven Wereley, an associate professor at Purdue University used a computer analysis (particle image velocimetry) to arrive at a rate of 70,000 barrels (2,900,000 US gallons; 11,000,000 litres) per day (plus or minus 20%).[76][77] However, after watching newly released video, on May 19 he said, "I can't say how much in excess of that 70,000 this leak is, but I would use the word 'considerable'".[78] In Congressional testimony, Werely stated that oil is escaping at the rate of 95,000 barrels — 4 million gallons — a day, nearly 20 times greater than the 5,000 barrel a day estimate BP and government scientists have been citing.[79]
A U.S. congressional panel heard testimony from experts including Wereley, who stated that estimating the rate of flow "is not rocket science," adding "all outside estimates are considerably higher than BP's." BP Chief Operating Officer Doug Suttles said on Wednesday, May 19, 2010 that BP's 5,000 barrels (210,000 US gal) a day estimate was "highly" uncertain.[80]. On May 20, BP admitted that its own internal estimates of the rate of the spill were greater than 5,000 barrels (210,000 US gal) per day and was already capturing 5,000 barrels (210,000 US gal) per day.[81] On May 20, after telling BP they would host the live feed if the company itself could or would not, United States lawmakers started streaming live video of the Gulf oil spill from 5,000 feet (1,500 m) below sea level.[82]
tl;dr - There's no way it's even close to the 5,000 a day that BP are saying, and we're likely to never find out the truth.