Oanh N. Pham, Joseph DeVincentis, Theodore Hwa, Robert Abbott, and Jim Boyce solved the problem.  My favorite answer is by Jim Boyce:
2,4,6,8,10  vs  3,7,9,11    (1,5,12,13)
1,4,6,9,13  vs 2,8,11,12    (3,5,7,10)
1,6,8,9,11  vs 5,7,10,13    (2,3,4,12)