Well she made the mistake of dividing the coefficient and the variable with the exponent wrong. we can look at this like (10 * x^-5) / (-5 * x^10)
we can actually factor out the 10 and the 1/-5 ans get 2 fractions to see this clearer. (10 / -5) * (x^-5 / x^10)
we can clearly say 10/-5 = -2
now the other one. when stuff that has exponents, as long as they have the same base we just subtract the exponents. so: (x^-5 / x^10) = x^(-5 - 10) = x^-15