C3PX said:

I really liked the first four seasons.

Maybe I gave up too soon by quitting after the first two DVD movies (which would be the first half of season five, I guess?)

The first two DVD movies are the first half of season five, yes.

The DVD movies were aired on Comedy Central in blocks of 4 split-up episodes to a movie (so "Bender's Big Score" becomes "Bender's Big Score, Part 1," "Part 2," "Part 3," and "Part 4"), though instead of waiting for all 4 movies to be done and airing them as a 16-episode season, they aired each movie separately as 4 episodes in a row (so, 2-hour blocks).

Regardless, the movies are production code 5ACV01-5ACV16, and the current season is 6ACV01-6ACV12 (with 6ACV13 being the Christmas special, and 6ACV14-6ACV26 airing next year, further confusing the question of how many seasons Futurama has).