Answer
$(z-x+5y)(z+x-5y)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $z^2-(x^2-10xy+25y^2)=\\=(z)^2-((x)^2-2\cdot5y\cdot x+(5y)^2)=\\=(z)^2-(x-5y)^2\\=(z-x+5y)(z+x-5y)$