To find the quotient function and evaluate it for the functions $f(x) = x^2 - 5x - 36$ and $g(x) = x + 4$: Step 1 — Find $(f/g)(x)$. Use the definition $(f/g)(x) = \frac{f(x)}{g(x)}$ and substitute the polynomials to form the expression $\frac{x^2 - 5x - 36}{x + 4}$. Perform polynomial division to obtain the quotient. The result is $x - 9$. Thus, $(f/g)(x) = x - 9$. Step 2 — Evaluate $(f/g)(-5)$. Substitute $-5$ for $x$ into the simplified quotient function: $(f/g)(-5) = (-5) - 9 = -14$.