Can the product and sum of a set of digits identify them uniquely?

Can two (or more) different sets of five single digit numbers have the same product and sum of all their digits at the same time?

ie.

1,4,8,4,3 (Product = 384, Sum = 20)

2,5,3,1,9 (Product = 270, Sum = 20)

The sums are the same but the products aren’t so these two sets don’t.

Furthermore, does the answer differ for other sized sets of single digits, can you find two different sets of any amount of digits that have the same product and sum?

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I just realised that it's possible with 3 or more digits and at least one as a 0. But if none of the numbers were 0?