Answer
$-\infty$
Work Step by Step
$$\lim_{x \to 2^{-}} \log_{5}(8x-x^{4})$$
$$\lim_{x \to 2^{-}} \frac{\ln(8x-x^{4})}{\ln 5}$$
$$\frac{1}{\ln(5)}\lim_{x \to 2^{-}}\ln(8x-x^{4})$$
$$\frac{1}{\ln(5)}\ln(\lim_{x \to 2^{-}}(8x-x^{4}))$$
$$\frac{1}{\ln(5)}\ln(\lim_{x \to 2^{-}}x(2-x)(4+2x+x^{2}))$$
Since $\lim_{x \to 2^{-}}x(2-x)(4+2x+x^{2})=+\infty$ it follows:
$$\frac{1}{\ln(5)}\ln(\lim_{x \to 2^{-}}x(2-x)(4+2x+x^{2}))=-\infty$$
