Evaluate `lim_(xtoa) ((x+2)^(5//3)-(a+2)^(5//3))/(x-a).`

Explanation

To evaluate the limit

\[ \lim_{x \to a} \frac{(x+2)^{5/3} - (a+2)^{5/3}}{x - a}, \]

we first notice that substituting \(x = a\) directly into the expression gives us a \(0/0\) indeterminate form. Therefore, we can apply L'Hôpital's Rule, which states that if we have an indeterminate form \(0/0\), we can differentiate the numerator and the denominator separately.

...