This is a statistic used by many advanced football analysts to determine how effectively a team holds possession of the ball. It counts the total number of drives, scoring or non-scoring, in which the team has possession of the ball for at least five minutes of game time. A team with a high number of five minute drives is said to have good ball control, and typically has a high degree of offensive efficiency.
There is no official documentation on why a mark of five minutes was chosen, but it was most likely because it is an easy number to use and marks exactly 1/3 of a quarter. Knowing how many five minute drives a team completes in a game is helpful because a team in possession of the ball is keeping the ball away from their opponent.
Even if a team has a weak offense, they have a better chance of winning if their offense can at least hold on to the ball for an extended period of time. Keeping the ball out of your opponent's hands keeps them from scoring.