How should I mic dance instructors when video recording?
There is another option that is good to know about, the Crown PCC-160 boundary mic. This is a standard mic to put at the edge of a stage to get good quality sound from actors in plays.

"Supercardioid pattern with PCC boundary technology assures phase coherence throughout the audible spectrum" means that it is rejecting sound from behind, and the phase coherence means that voices are more clear than with normal mics, as long as you place them at a boundary like the floor or on a wall. Physics stuff.

Lavs will get you the most clear sound, but the Crown PCC will do better than a shotgun (unless you have the shotgun close with a boom pole). Rent a pair to try them out as backup, I think you will want to buy them after you see how effective they are.

Edit: Rereading your question, if the dancers are confined to a 5x5' area and they might be speaking with their back to the camera, lav is the best, but next best is probably a boom mic on a stand, with the mic positioned directly over the center of the area, pointed straight down. That should pick up a pretty balanced voice recording. A second shotgun positioned in line with the camera to get the front 'viewpoint' audio would capture a more natural-sounding voice when the speaker is speaking toward the camera. The Crown PCCs would have to be positioned all around the area, and they would pick up more of the dancer's feet sounds than the boom mic.