a^{5}(b-c)+b^{5}(c-a)+c^{5}(a-b)

Step 1 ：Given expression is \(a^{5}(b-c)+b^{5}(c-a)+c^{5}(a-b)\)

Step 2 ：Rearrange the terms to group similar terms together, we get \(a^{5}b - a^{5}c + b^{5}c - b^{5}a + c^{5}a - c^{5}b\)

Step 3 ：Factor out common terms, we get \(a^{5}(b-c) + b^{5}(c-a) + c^{5}(a-b)\)

Step 4 ：This is the simplest form of the expression, so we can't simplify it further

Step 5 ：Check the result, substitute arbitrary values for a, b, and c into the original expression and the final result, they should be equal

Step 6 ：Therefore, the final result is \(\boxed{a^{5}(b-c) + b^{5}(c-a) + c^{5}(a-b)}\)