In rugby, why is a fly-half called "first five eighth"?

This is uncommon in the Northern Hemisphere.
Rugby teams are basically split in to forwards and backs, the backs are nominally split again into half backs and three-quarters.

New Zealand saw advantage in having a fourth player in the three-quarters placing a forward between the half back and the three-quarters. Legend has it that the position was named by deciding that the half back was 4/8ths and the three-quarters 6/8ths, so therefore the new position must be a 5/8ths. When fly half play developed they introduced the first 5/8th and the second 5/8th. Hence the fly half is sometimes referred to as the 1st 5/8, implying a slightly deeper position than halfback and the inside centre is sometimes referred to as the 2nd 5/8 implying a more forward position than a 3/4 back.

http://www.rugbyfootballhistory.com/positions.html