The difference \( \log _{5}(32)-\log _{5}(4) \) can also be expressed as \( \log _{5}(8) \) \( \log _{5}(28) \) \( \log _{5}(12) \) \( \log _{5}\left(\frac{4}{32}\right) \)

To simplify \( \log_{5}(32) - \log_{5}(4) \), we can apply the property of logarithms that states \( \log_{a}(b) - \log_{a}(c) = \log_{a}\left(\frac{b}{c}\right) \). Hence, we get: \[ \log_{5}(32) - \log_{5}(4) = \log_{5}\left(\frac{32}{4}\right) = \log_{5}(8). \] So the correct option is \( \log _{5}(8) \). Now, it's also worth noting that \( 32 \) can be expressed as \( 2^5 \) and \( 4 \) as \( 2^2 \). This means \( \frac{32}{4} = \frac{2^5}{2^2} = 2^{5-2} = 2^3 \), which is \( 8 \). Such transformations can make logarithmic calculations much simpler and can add to your mathematical toolkit. If someone were to confuse the logarithmic subtraction as directly resulting in \( \log_{5}(12) \) or \( \log_{5}(28) \), remember that those values are products or composites of the original bases rather than simple divisions or subtractions! Understanding how properties of logarithms work will help clear up potential mishaps in calculations.