Q:

Why was Season 5 of Futurama composed of films?

Why was it that season 5 of Futurama was entirely composed of films? 

A:

Futurama was cancelled on Fox in 2003 when it decided to stop buying episodes midway through the fourth season.  Technically the show was never officially cancelled.
In 2005, Comedy Central acquired the syndication rights to Futurama.
 In 2006, it was announced that four straight-to-DVD films would be produced, and later split into 16 episodes comprising a new season.
In June, 2009 Comedy Central picked up the show for 26 new half-hour episodes that began airing on June 24, 2010

A:

Claudia Katz, a producer on Futurama and partner of the studio that animates Futurama, Rough Draft Studios, explained in an interview back around the time of the first film's release:

Claudia Katz: Probably the most important component was, I believe, when Comedy Central started sort of negotiating for the cable window rights and Fox said, "Hey, would you be interested in new episodes?" They sort of agreed to commit to 16 new episodes. At that time we were sort of negotiating on these DVD movies and there was a question of doing 2 or 3, then it looked like it was going to be 3. I think when Comedy Central committed to the 16 it turned into 4 because, really, each of these DVD movies is going to be sort of divided into 4 episodes. Honestly, part of the reason is also economics. It's sort of the more of them we do the greater the economies of scale are.

So when Fox asked Comedy Central if they wanted new episodes, Fox had already started the process of producing some direct-to-DVD Futurama material.  Comedy Central's success with the Futurama syndication meant they were interested in helping to finance new Futurama.  The format of 4 movies was chosen as it was what was already in motion, and the economies of scale for producing 4 movies instead of 16 individual episode made the proposition more affordable.

