Yep, they'll fit on a P5. It's kinda common around here for MSPs to run the stock P5 wheels as part of their winter/snow setup -- so yep, same lug pattern and all that.
You can still get a fairly 'tall' tire even on a 16". I believe I have a 50 series on mine -- it might even be a 55, I can't remember exactly, I'll have to go check -- but it's plenty of rubber for the winter.
Anyhoo, like I said, I probably won't have the steelies available for a few months. But if it's anything pressing, I can try to see how soon I can have my winter tires moved from the steelies to my Mazda3 wheels.
I'm located in Lancaster, PA by the way .. but I grew up in the northeast Philly suburbs and am back in the area once every couple months to visit friends and family, so we can prolly meet up at some point for you to pick up the steelies, so we don't even have to worry about shipping.