They have 5 to play 4
There are some examples of people graduating and being given and extra year of eligibility (Florida player about 10 years ago) and there was a guy who played/was on the basketball team for NC State 7 years.
For the OP there are also "medical redshirts" which often are for catastrophic injuries early in a season-these have to be applied for
They changed the rules about 15 years ago too so that a guy can play minor league (paid) baseball but still playing college football.
There are a few examples of guys going completely pro but returning for another sport-a Georgia quarterback a while ago and Tim Dwight in the NFL who went back to run track at Iowa
This is an interesting case
Marcus Monk is currently on the Arkansas basketball team.
Marcus Monk (born April 26, 1986 in Lepanto, Arkansas) is a American football wide receiver who is currently a free agent. He was drafted by the Chicago Bears in the seventh round of the 2008 NFL Draft and was also a member of the New York Giants.
After not playing for an NFL team, Monk received permission to return to college for his final year of basketball eligibility. He is a current basketball player for the Arkansas Razorbacks.
Professional career
Chicago Bears
Monk was selected in the seventh round (248th overall) of the 2008 NFL Draft by the Chicago Bears. Monk signed a four-year rookie deal with the Bears on May 31, 2008. He was waived on August 24.
On August 26, 2008, Monk was claimed off waivers by the New York Giants after the team waived/injured wide receiver Craphonso Thorpe. However, he was waived by the team four days later during final cuts. On August 31, he was re-signed to the team's practice squad. He was released from the practice squad on September 8 after wide receiver Taye Biddle was signed.
http://en.wikipedia.org/wiki/Marcus_Monk