Evaluate the following limit: `underset( x rarr 5) ( "lim")(x^3-125)/(x^2-7x+10)`

Explanation

To evaluate the limit \( \lim_{x \to 5} \frac{x^3 - 125}{x^2 - 7x + 10} \), we can follow these steps:

### Step 1: Factor the numerator and denominator
The numerator \( x^3 - 125 \) can be factored using the difference of cubes formula:
\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]
Here, \( a = x \) and \( b = 5 \). Thus, we can write:
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