Chapter 2.3, Problem 73E

Useful factorization formula Calculate the following limits using the factorization formula

$x^n-a^n=(x-a)(x^{n-1}+x^{n-2}a+x^{n-3}{a}^2+\cdots +x{a}^{n-2}+a^{n-1}),$

where n is a positive integer and a is a real number.

73. $\underset{x\to a}{\lim }\frac{x^5-a^5}{x-a}$