This is a most common but not to be avoided question asked by new mothers. The umbilical cord stump usually falls off within 5-7 days of the baby’s birth. For its care, you should air dry the stump. When the umbilical cord stump is there, you just sponge your baby’s body. If you find any puss or blood near the umbilical cord stump, you should consult your nearest pediatrician.