1. Problem: Determine the parity (evenness or oddness) of the function $$f(x) = \ln\left(\frac{5 - x}{x + 5}\right)$$. 2. Recall that a function $f$ is even if $f(-x) = f(x)$ for all $x$ in the domain, and odd if $f(-x) = -f(x)$. 3. Compute $f(-x)$: $$f(-x) = \ln\left(\frac{5 - (-x)}{-x + 5}\right) = \ln\left(\frac{5 + x}{5 - x}\right)$$ 4. Notice that: $$\frac{5 + x}{5 - x} = \frac{1}{\frac{5 - x}{5 + x}}$$ 5. Using the logarithm property $\ln\left(\frac{1}{a}\right) = -\ln(a)$, we get: $$f(-x) = \ln\left(\frac{1}{\frac{5 - x}{5 + x}}\right) = -\ln\left(\frac{5 - x}{5 + x}\right) = -f(x)$$ 6. Since $f(-x) = -f(x)$, the function $f$ is odd. Final answer: The function $f(x) = \ln\left(\frac{5 - x}{x + 5}\right)$ is an odd function.