Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.7 Exercises - Page 564: 14

$-\infty$

$\lim _{x\rightarrow 5^-}\dfrac {\sqrt {25-x^{2}}}{x-5}\dfrac {=\dfrac {d}{dx}\left( \sqrt {25-x^{2}}\right) }{\dfrac {d}{dx}\left( x-5\right) }=\dfrac {\dfrac {-2x}{2\sqrt {25-x^{2}}}}{1}=-\dfrac {x}{\sqrt {25-x^{2}}}=-\dfrac {5}{\sqrt {25-5^{2}}}=-\infty $