c. \( \lim _{x \rightarrow 5}=\frac{1}{(x-5)^{5}}= \)

As \( x \) approaches 5, the expression \( (x-5)^{5} \) approaches 0 because \( (5-5)^{5} = 0^{5} = 0 \). Since we are looking at \( \frac{1}{(x-5)^{5}} \), we are effectively dividing by a number that gets closer and closer to zero. This means the limit will diverge to infinity in absolute value, resulting in \( \lim _{x \rightarrow 5} \frac{1}{(x-5)^{5}} = \pm \infty \), depending on the direction from which \( x \) approaches 5. However, since \( (x-5)^{5} \) approaches 0 with a positive exponent, we find that as \( x \) approaches 5 from the right (values greater than 5), \( (x-5)^{5} \) is positive and we approach \( +\infty \). Conversely, as \( x \) approaches 5 from the left (values less than 5), \( (x-5)^{5} \) is negative, so we approach \( -\infty \). Therefore, the limit does not exist in the conventional sense, as it depends on the direction of approach.