I would be really surprised if your baby was getting anything from the placenta after 5-15min from birth. Most often, even a placenta that has not fully released is still done working within that time frame. Of course, there are tons of 'variations on the norm', and birth often has variations that are particular to the needs of the mom/baby involved, so I don't exactly rule out the possibility that your baby really did keep on with an exchange through the placenta. Still, I find myself very curious--did you check the cord for a pulse at all? Did you note what the cord looked like?
A 'working connection' will show a cord with color and 'life'--blue-ish usually, bluey silver; and it will be firm, have some body--it's kind of like a live snake, I think. There will be a pulse that can be felt when you hold the cord--a pulse at the same normal rate as baby's heart rate (so, approximately 120--160per minute, more or less). Once the placenta is done working, first thing is usually that the pulsing stops--or it becomes slow and erratic before stopping entirely. Also, the cord becomes limp and white and much thinner than it was at birth. It loses color and firmness. gets thinner, because nearly all of the blood has drained out of it.
While there is seldom any reason to rush the clamping/cutting of the cord (and of course lotus birthers never do at all), I usually see cords 'ready to cut'--thin, white, limp--within 10 min of birth. Occasionally longer--but I don't think I've ever seen a cord show any sign of life beyond 15or so min. from birth. This is true even at births where baby was born in some degree of distress, not breathing well or something.
Again, just curious here. I've never heard of, or seen a placenta keep functioning as long as you say, it's a fascinating possibility! If there is anything you can say about what I've mentioned above (if you noticed any of the signs--maybe you were far busier noticing the baby), I'd love to hear it--pics would be even better, if you have any of you/baby in that first hour after birth that might also show the cord.