Simplify the expression. Assume that all variables represent positive integers. ${\left(x^{y+5}\right)}^{y-5}$

A) $x^{y^2-s^2}$
B) $x^{y^2+2y5+5^2}$
C) $x^{y^2+s^2}$
D) $x^{y^2-2y5-5^2}$
E) $x^{y^2+2y5-5^2}$

When simplifying the expression ${\left(x^{y+5}\right)}^{y-5}$ , use the power of a power rule, which multiplies the exponents: $(x^m{)}^n=x^{mn}$ . Thus, ${\left(x^{y+5}\right)}^{y-5}=x^{(y+5)(y-5)}$ , which simplifies to $x^{y^2-25}$ using the difference of squares formula $(a+b)(a-b)=a^2-b^2$ . None of the provided options exactly match this simplification, but option A, $x^{y^2-s^2}$ , is the closest in form, suggesting a typographical error in the options. The correct mathematical simplification should be $x^{y^2-25}$ .