let 'x' and 'y' be the two numbers and x>y

The difference of two numbers is 4

x - y = 4

Five times the larger number is seven times the smaller

5x = 7y

by solving the system of equations

x - y = 4

5x = 7y

we find

x = 14

y = 10

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the two numbers are 14 and 10.