The 5,280 feet to a mile ratio, which drives school children crazy (and their parents too), started in ancient Rome. The Romans, who measured distances in paces, had a measurement called "milia passuum," Latin for "a thousand paces." Since each pace was 5 feet, a milia passuum was 5,000 feet.
Makes sense so far, right? But then the British got involved.
British farmers measured their land in furlongs, with each furlong measuring 660 feet. When they adopted the milia passuum--abbreviating the name to "mile"--they decided that it should equal a whole number of furlongs. They could have made a mile equal 8 furlongs and then cut each furlong down a bit--keeping 5,000 feet to the mile and making things easier for us today--but they didn't. Instead, they lengthened the mile to 8 full furlongs, or 5,280 feet.
I guess you can't really blame the British. If a deed measured my land in furlongs I wouldn't shorten furlongs to accommodate the mile either.