If you have the same season-ending injury twice, you can receive a sixth year. Two different injuries I am not sure, but I know having the same season-ending injury twice is significant to the NCAA. This was the case with a runner on my team in college. Now I don't know what the NCAA counts as "season-ending", but one of the key factors from what I remember about my teammate's, and my own, experience applying for a redshirt was that the doctor that evaluates the athlete must deem the injury season-ending, or at the very least DOCUMENT that the athlete's recommended course of action is to stop competing. This was a big hangup for me as the training staff at my school did not do a great job with the docementation, but my teammate had excellent documentation and received a 6th year (mine was only for a 5th year). From what I remember, very obvious season-ending injuries (ligament tear, serious lower leg fractures, etc) are handled pretty quickly by the NCAA, and there isn't much debate over whether or not that person will get their redshirt. Where it gets hazy is when the injury isn't deemed to be season-ending by the doctor, but they recommend the athlete stop competing for a certain period of time. This happened to me, and it took over 6 months for the NCAA to finally award me a redshirt. I also know that a big concept the NCAA uses in deciding on medical redshirts is whether that athlete had a "fair and legitimate" chance to compete for four seasons. This concept helped me, as I missed about 7 weeks with my injury, but the NCAA deemed that it prevented me from having a fair or legitimate chance at competing in outdoor track. This is probably more info than we asked for in this thread but oh well.
If one of those redshirts wasn't due to medical reasons then he is done