Answer
At $-1$: $\frac{1}{8}.$
The domain is all real numbers except $-12$ and $3$.
Work Step by Step
We plug in $x=-1$ to $f(x)$ to get $f(-1)=\frac{-1-4}{(-1)^2+5\cdot(-1)-36}=\frac{-5}{1+(-5)-36}=\frac{-5}{-40}=\frac{1}{8}.$
We know that $x^2+5x-36=(x+12)(x-3).$
We know that the denominator cannot be $0$, hence $x+12\ne0$ and $x-3\ne0$, thus $x\ne-12$ and $x\ne3$.
Thus the domain is all real numbers except $-12$ and $3$.
