Hi E Hilton,
I am currently in the middle of a 800sf install of 3 1/4 hardwood. Checked my actual nailing usage last night and found that I have used 4000 nails to do 560sf so far.
That works out to 4000nails/560sf = 7.1 nails/sf.
Now if your boards are 5", you will need less nails. I would calcuate that you require 7.1 nails/sf x 3.25"/5" = 4.6 nails/sf.
Therefore, for a 500sf install that works out to approximately 4.6 nails/sf x 500sf = 2300 nails - which is in good agreement with your calculations.
I would order 3 boxes of 1000 and you should be good to go!
Note that I hand drilled and nailed my starter rows and finish rows - so I did not account for this in the above calculations.