your phone may be stuck in headphones mode, try plugging and unplugging the headphones a couple of times, also try holding the sleep/wake button and home button at the same time until the phone restarts.
The iPhone 5 includes a single speaker as with all previous iPhone models.
You discovered this is a "major" issue with the iPhone 5 where? I haven't seen this reported here in great numbers.
Have you tried removing and reinserting the earbuds several times in a row? The mechanism that turns the external speaker off when earbuds are inserted may be stuck in place.
If so with no change, the iPhone includes a one year warranty. Call AppleCare or make an appointment at an Apple store if there is one nearby.