There are only 2 ways.
first of all, it says that order does not matter, which means that 5 5 5 2 is the same as 2 5 5 5.
second, there are just 2 ways, once you consider parity. 5 5 5 2 and 5 2 2 2 2 2 2. you cannot have 2 fives, because if you do, once you add the 2s, it will stay even, and 17 is not even.
therefore, there are only 2 solutions