First, establish a consistent bedtime ritual, building on things that are familiar to her. Avoid over-stimulating her for about an hour prior to her designated bedtime. Offer a light snack or drink and then do personal hygiene--bathing or washing up, changing into pajamas, brushing teeth, and changing diapers or using the toilet. Finish with calming and soothing activities like rocking or reading stories. She may enjoy cuddling with a doll, soft toy, blanket, or stuffed animal to ease the transition to sleep. Put her into bed with this "transitional object" while still awake, so she learns to put herself to sleep. The room should be quiet, dark (except for a night-light if desired), and cool. After saying goodnight, leave the room.
Now, what about the screaming? Is she tired? Since she falls asleep in five minutes, it seems unlikely that her screaming is because she is not tired. To encourage a regular sleep pattern, try waking her at the same time each morning. At this age, one afternoon nap of no more than two hours should be sufficient.
Is she screaming to get attention? If you stay in her room or extend her bedtime ritual, she interprets her screaming as successful. It would be better to leave the room and ignore her crying (though it may get worse before it gets better).
Does she seem afraid? After putting her in bed, you may want to sit quietly in the room until she falls asleep. Did she watch something on TV or have a book read to her that she interprets as scary? Talk about her fears during the daytime. Focus on more pleasant things. As she learns to fall asleep without fear, move your chair farther from her bed.
Remember, this won't be solved "overnight." Be patient, and try to be consistent. Good luck!