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Yes, you could.
This could be easily proven algebraically, but I'm too tipsy.
The problem does not state that the wire has the be evenly gapped around the earth (which is assumed)- if this were the case, no way. But if the wire was zero mass and zero thickness, it could easily be pulled taught until all the slack was in once place, and the wire met, with 5 feet of slack overlapping for a total of 10 feet of slack. Plenty of room for a finger.
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