This question is classic FOIL method, used for multiplying 2 binomials. You will multiply 4 times and combine any like terms to get your answer.
FOIL stands for First Outer Inner Last... You multiply the first terms in each set, then the outside terms, then the inside terms, then the last terms.
In this case...
F is x*x^4
O is x*-y^4
I is y*x^4
L is y*-y^4
Multiply these together following the rules of exponents, separating them with addition, then combining any like terms.