As for the first question, IMO it refers to fifth grade.1. Does "fifth year" mean "fifth year in career" or "fifth grade teacher"?
2. "To the bank" definitely means "to the construction by the dam or river" differentiated from the second bank for pun, right? See definition #4 of "bank" here
3. What is the difference between "run to" and "run down to"? In this case, following the definition in the link I provided, it literally means that the bank was at a lower level to the place where the woman was.
ex)A fifth year teacher was giving his elementary school students a lesson to develop their logical thinking. "This is the scene," said the teacher. "A man is standing up in a boat in the middle of a river, fishing. He loses his balance, falls in, and begins yelling for help. His wife hears him screaming, knows he can't swim, and runs down to the bank. Why do you think sh ran to the bank?" The teacher said to students. "Guess what the answer might be." A little girl raised her hands and asked. "To draw out all his savings."
Student or Learner