You have 5 balls that you have to divide (put the balls in the cups) between a number of cups in all possible ways.

1 cup:
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|5|
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1 possibility
Total: 1 possibility

2 cups:
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|1|4|
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|2|3|
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|3|2|
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|4|1|
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|5|0|
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|0|5|
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6 possibilities
Total: 7 possibilities

3 cups:
21 possibilities
Total: 28 possibilities

Continue until you have 500 cups. The total of possibilities from 1 to 500 is the answer.