There are many possible answers.
One is 5, 7 and 7499
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The sum of three odd numbers will be odd, whether they are prime or not. The sum of three prime numbers can be even as long as one of them is 2.
The sum of the first five prime numbers is 28. The sum of the cubes of the first three prime numbers is 160. The average of 28 and 160 is 94.
12
2,2,5
Two prime numbers can have only one sum, not three different sums!