While I would argue that most of the time this is just personal choice, there is an actual advantage of choosing speed 5 (or any other speed that is a power of two + 1) over speed 6: It is easier to slide to any note using portamentos (commands E/F or 1/2) with easy-to-remember parameters. One portamento unit is 1/16th of a semitone, so at speed 5 you can slide on one semitone in one row using F04, or two semitones with F08, etc... at speed 6 the math is more complicated and often you need a fine slide on the next row to reach the wanted note.
But as said, most of the time it's just personal choice. Back in the very early days of MODs, the only way to set the tempo of a song was by changing the ticks per row, so if you wanted to be slightly faster than speed 6 / tempo 125, the only option was speed 5 / tempo 125, and not something like speed 6 / tempo 140. Speed 3 and 6 are most often chosen because they result in "true" BPM (or at least close enough to true BPM) with classic tempo mode.
