The widespread practice of eating food dropped on the floor if it is picked up in under 5 seconds has no validity. No matter how short the contact period is, food dropped on the floor will pick up some bacteria from the floor. The longer the food stays on the floor, the more bacteria it will gather, but it will always gather some even if picked up immediately.
But does that gathered bacteria matter?
In 2004, a Chicago student was awarded an Ig Nobel prize in public health for performing standardized food drops on a floor at the University of Illinois. Her first attempts did not find enough bacteria on the floor for a valid test, so she was forced to grow bacteria colonies on the floor and then perform her experiment. The results both disproved the 5-second rule and proved that the floor was surprisingly clean.
Most homes don’t have a professional custodial staff to perform nightly cleanings, however, so those results may not be widely applicable. Also, the test floor was made of tile, and surface material impacts the bacteria found upon it. A study of Texas public restrooms found that it was much more difficult for bacteria to grow on metal surfaces as opposed to plastic surfaces. Other conditions also mattered, especially moisture on the surface. An attempt by a doomsday cult to intentionally spread salmonella in Oregon via doorknobs was unsuccessful (although the cult did eventually gain limited success by infecting a salad bar). The dry, smooth doorknob surface fortunately (or unfortunately, for the cult) inhibited bacterial growth.
But the question remains: does it matter? Studies have shown that bacteria are pretty much everywhere. So really, gathering bacteria from the floor may be moot when it comes to food, as most food already has bacteria on it. A widely-used high school biology lab experiment has documented that most produce is already covered in various strains of bacteria. For the most part, washing does not matter—the bacteria, some of which can cause intestinal distress, are present regardless of washing.
The trick is limiting harmful bacteria. Keep floors clean, and if you, say, drop a raw chicken, disinfect the area. Keeping floors dry will also help. Keep in mind that documented cases of illness linked to dropped food are extremely rare. But maybe try not to eat off the floor anyway? It is the floor, after all.