The larger number is 22 while the smaller number is -17.
Let x represent the larger number and y represent the smaller number.
The sum of two numbers is 5, hence:
x + y = 5 (1)
The larger difference of the two numbers is 39, hence:
x - y = 39 (2)
Solving equations 1 and 2 simultaneously gives:
x = 22, y = -17
Therefore the larger number is 22 while the smaller number is -17.
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