The 1905 cent was made of a .950 copper alloy. The remaining .050 consisting of tin and zinc. While the specific percentages of either zinc or tin frequently varied, the combined total rarely exceeded .070.
What can make a copper cent appear white? There are dozens, if not hundreds of environmental conditions that can affect the surface of the coin, giving it an abnormal appearance. A trick we used in grade school was to coat coins in mercury, giving the coin a silvery appearance. Over time the mercury would alloy (is this the right term?) itself with the copper, lessening the silvery appearance and becoming more white, somewhat similar to zinc.
Deliberately plating is also a possibility.
The most likely possibility is an old (references go back to Roman era) chemistry experiment demonstrating simple plating techniques using zinc sulfate or zinc chloride. Do a general Internet search on how to turn a penny white (or red, or gold). There will be dozens of links on how to do it, including YouTube videos.