What allegedly happened, well...this is how you get on Ellen, period.
Anything is possible, but this story not probable. 5 miles is a huge exaggeration. If she had said 1 mile, people would have still been skeptical.
The cubs could not have kept up anywhere near 5 miles and the bear would have lost interest long before that.
If the tree were too small or the branches too weak for a bear to climb, the bear could easily have pushed the tree back and forth till it toppled or shook her out of it (yes, they can do that---research it).
Most likely, she saw the cubs, saw the Mama bear and ran. If she truly climbed up a tree, her body would surely have evidence of that with scraps and marks from the bark. If she did, it doesn't mean that the bear was anywhere near her.
Bears can't run quickly around larger things, like a big tree, like a dog can do. Ponder that.