Emily has been waiting for a promotion to a management position for almost 5 years she noticed that man fill most of the higher level jobs in her company she suspects she is not being promoted because she's a female what term describes this

The term that describes this situation is glass ceiling.

Glass ceiling is a term used to refer a barrier that impedes a person, generally a woman, from improving her position at work. In other words, it makes reference to an unjustified barrier that prevents a woman from making progress in her profession for being considered "less motivated and dedicated" than a man. It is closely related to a form of discrimination, that is misogyny. It is believed that the first person that used the term "glass ceiling" was Marilyn Loden in 1978.