With five numbers there are 5 ways to group 4 of them together. If you take the averages of each group of 4 numbers and get...

3428.5
3425.75
3398
3120.25
342.5

What are the 5 numbers?

By multiplying all of the averages by 4 I elimanated the division by 4 when you take the average and set up the following system.

a+b+c+d=13714

a+c+d+e=13703

a+b+d+e=13592

a+b+c+e=12481

b+c+d+e=1370

By solcving this system of equaitons you will arive at the fact that the five numbers are.

1, 12, 123, 1234, 12345