I have an opportunity to purchase a 16" 5 HP Power Mate planer, but it is 3-phase. Can I convert it to single phase?
It is easy to convert single phase to 3-phase to run the planer. You can usually find phase converters used or buy a new one. You can also make your own with another 3-phase motor.
Woodworking tools such as planers and saws are more demanding than metal tools because they usually require a higher percentage of available torque from the work motor. For this reason, it is advisable to build your phase converter from a high-speed (3600) 3-phase motor, at least as large as the work motor. Bigger wouldn't hurt.
This is done frequently. It's much cheaper than buying commercial units. I have been using phase converted power for 30 plus years in my machine shop.