Find the limit. \( \lim _{x \rightarrow 5^{-}} \frac{1}{x+5} \)

To find the limit \( \lim _{x \rightarrow 5^{-}} \frac{1}{x+5} \), we evaluate the expression as \( x \) approaches 5 from the left. As \( x \) gets closer to 5 from the left (meaning \( x \) takes on values just slightly less than 5), we can substitute \( x \) with values close to 5, such as 4.9, 4.99, etc. When \( x \) approaches 5, the expression simplifies as follows: \[ x + 5 \rightarrow 5 + 5 = 10 \] Thus, the limit becomes: \[ \frac{1}{10} = 0.1 \] So, the final result is: \[ \lim _{x \rightarrow 5^{-}} \frac{1}{x+5} = 0.1 \]