How to factorise x^5-y^5 ?????

The given polynomial is x⁵ – y⁵.

Putting x = y, we get 

x⁵ – y⁵ = x⁵ – x⁵ = 0 

∴ (x – y) is the factor of x⁵ – y⁵.            (Factor Theorem)

Thus, (x⁵ – y⁵) = (x – y) (x⁴ + x³y + x²y² + xy³ + y⁴)