Mostly, Jung is making stuff up based on an unfounded assumption that we can best understand kids by assuming they have sexual fantasies about their parents and that most things that are wrong with them are because these fantasies are somehow unresolved.
Jung's theory about girls is called Electra complex, based on Freud's Oedipus complex (originally applied to boys, though also expanded to include girls; Freud disagreed with Jung that they should be named separately).
As written in Wikipedia:
There is very little scientific evidence for the reality of the Electra complex. The predictions of the theory are not substantiated by experiment.[21][22] The Electra complex is not widely accepted among modern mental health professionals and is not listed in current versions of the Diagnostic and Statistical Manual of Mental Disorders.[23]
Earlier in the book, Jung talks about a dream the girl had:
At the third interview the little girl related a dream she had
had when she was five years old, and by which she was greatly
impressed. She says, "
I'll never forget this dream." The dream
runs as follows : "
I am in a wood with my little brother and we are looking for strawberries. Then a wolf came and jumped at me. I took to a staircase, the wolf after me. I fall down and
the wolf bites my leg. I awoke in terror."
In your quote, "she had this dream in her fifth year" is referring to this dream. Jung says this sounds like the "well-known German fairy-tale of Little Red Ridinghood, which is, of course, known to the child". He goes on to talk vaguely about a broader astro-mythological context to fairy tales and mythology and then jumps to:
These currents are caused by the libido in its unconscious forms. The material
which comes to the surface is infantile material, hence, phantasies connected with the incest-complex.
Jung has no evidence for this, Freud has no evidence for this, they just say it and then start interpreting everything as based on this, kind of like a conspiracy theorist would. It's an absolutely terrible way to go about actually understanding the world, and not at all how science works.
Other statements seem a bit more believable at face value:
The fear of the wolf in the dream is therefore fear of her
father. The little patient explains her fear of her father by his severity towards her. He had also told her that we only have
bad dreams when we have been doing wrong.
Basically, her father is "severe" towards her - maybe that means he yells at her, maybe it merely means he is strict about her behavior, maybe it means he is physically imposing or abusive; the details are not given. But it seems he has told his young daughter that if she has bad dreams it means she's doing something wrong; I can imagine that making a kid feel pretty uncomfortable by itself. What Jung thinks is more important than that, though, is this sexual obsession she has with her father.
As far as what happened to her in her fifth year? It's right in your quote:
Her youngest brother was born at that time
He elaborates:
This dream illustrates the first impressive appearance of the sexual problem,
obviously suggested by the recent birth of the little brother, just
such an occasion when experience teaches us that these questions
become vital.
So in other words, Jung says girls are sexually obsessed with their fathers, "obviously" having a sibling born surfaces these obsessions, and so all this trouble has magnified around when the girl is 5.
