Tax advise needed on 5 year old rental property

[Erica Hill]

I purchased a single family home in AZ in 2013 for my mother. I resided in MO at the time. My mother pays rent but the house is in my name. I never registered the property as rental in AZ (I didn’t know I needed to) nor have I treated it as investment property on my taxes.  Do I need to register the property and reflect this property on my taxes as an investment property (I don’t currently write off anything but mortgage interest and taxes.  if so, how do I handle 2013 - 2016?  If I Sale the property am I going to get hammered for depreciation even though I never took it? 

Additionally, I plan to purchase another property which will either be my primary residence in NH or another investment property in FL this year.  Note neither will be in AZ.  

Any and all suggestions are appreciated. Thank you in advance!