A "fifth-year senior" is slang for students in their fifth year of study at a program designed to be completed in four years. It often results due to failed coursework or not taking a full workload.
In the world of college athletics, the term also refers to student-athletes competing in their fifth year of eligibility at their respective academic institutions. This typically occurs when the student redshirts, or takes a year off due to an injury or a lack of anticipated playing time. Through a waiver, the student may be granted a fifth year of eligibility by the governing body, such as the NCAA or NAIA.