Comet Lucifer is an anime series that started during the Fall 2015 season. The series is uncommon given that it isn't an adaptation of a manga or light/visual novel, so it's a fresh story.
Here's the MAL link:
http://myanimelist.net/anime/31318/Comet_Lucifer
The basic summary is a boy (Sogo) happens upon a large stone that has a sleeping girl in it; said stone shatters, freeing the girl within. This girl (Felia) is physically a child, with her mental capability being that of a newborn (she had to learn pretty much everything from the boy and his friends). Felia also has some kind of telekinetic power. It's a pretty light-hearted adventure story that includes mechas.
Now, onto the AP. In episode 5, Felia is seen in a giant sphere while Sogo is trying to reach her. Sogo encounters danger and Felia decides to use her powers to rescue him. She seemingly used too much of her power (or maybe she unlocked more of her power? Who knows) and it causes her to both physically and mentally progress to that of a teenager (or young adult?).
There is no sequence, just an off-screen transformation. The first image is from the opening credits (because I couldn't find a good enough full-body shot of Felia within that episode) while the second image is found towards the end of the episode.