Abinomial is multiplied by a third degree trinomial. what degree must be in order for the product to have a degree of 5 ?

Okay, so we don't know the degree of a binomial, but we do know that the degree of the trinomial is 3. We also know that the product has the degree of 5, which means that we just have to subtract 5 by 3 to get the degree of the binomial. So:

x^2 * x^3 = x^5 because since the variable is the same number, its degrees will add, not multiply. 
The degree of the binomial is 2.