Think you are wrong
Which part? Every student athlete has 5 years to play 4. Drew has already used his 1 redshirt year given to every incoming athlete. So when he started last year he basically had 4 years to play 4. Now, like I said he can petition to get a 6th year of eligibility but typically those are granted to kids with extenuating circumstances...i.e. transfers, multiple injuries, etc. Kids are typically only granted a 6th year if they miss multiple seasons for reasons beyond their control and optionally accepting a redshirt year your Freshman year when he was healthy and could have competed would not count in this situation.
12.8.1.5.1 Waiver Criteria. A waiver of the five-year period of eligibility is designed to provide a student athlete with the opportunity to participate in four seasons of intercollegiate competition within a five-year period. This waiver may be granted, based upon objective evidence, for reasons that are beyond the control of the student-athlete or the institution, which deprive the student-athlete of the opportunity to participate for more than one season in his or her sport within the five-year period.
Now, obviously this is the NCAA we're talking about and nothing is set in stone. UK could petition the NCAA and Barker could win another year. My only point is that its unlikely.