$\lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}$

Step 1 ：This is a limit problem. The function is not defined at x=5, but we can simplify the function by factoring the numerator and then cancel out the common factor in the numerator and denominator.

Step 2 ：First, we factor the numerator: \(x^{2}-25\) can be factored into \((x-5)(x+5)\).

Step 3 ：So the function \(\frac{x^{2}-25}{x-5}\) can be simplified to \(x+5\) after cancelling out the common factor \(x-5\).

Step 4 ：After simplifying, we can substitute x=5 into the function to find the limit.

Step 5 ：Substituting x=5 into the simplified function \(x+5\), we get \(5+5=10\).

Step 6 ：So, the limit of the function as x approaches 5 is 10.

Step 7 ：Final Answer: \(\boxed{10}\)