Actual "new old stock", never opened, never used?
As far as I can recall, AA batteries would not come installed in the mouse, and would be separately wrapped.
But, not really a hard issue.... Buy the mouse. Open the box. Inspect batteries. They should have a month/year for the suggested life of the battery in storage. If older than today's date, dispose of those batteries, and install new ones.
If I am incorrect, and the AA batteries come installed, then inspect the battery connectors, replace the batteries that came with the mouse..
If the batteries do come installed, and there's corrosion, then after more than 5 years, the mouse is likely useless to you, but then, a Magic Mouse is not that great of a prize to discover, is it? I have nearly a dozen Macs, and one Magic Mouse, which I use once or twice a year, usually for some kind of bluetooth checks (I pop the batteries out whenever I put it back in the box. I have no idea when it will "come out" next)