To differentiate $y = \log_5 x$ with respect to $x$, we can use the following derivative rule for logarithms:

$\frac{d}{dx} \log_b x = \frac{1}{x \ln b}$

where $b$ is the base of the logarithm.

Here, $b = 5$, so the derivative of $\log_5 x$ is:

$\frac{d}{dx} \log_5 x = \frac{1}{x \ln 5}$

This is the derivative of $y = \log_5 x$ with respect to $x$.

Would you like further clarification or details? Here are 5 related questions that may help expand on this topic:

1. How do you differentiate logarithmic functions with other bases?
2. What is the derivative of natural logarithms $\ln x$?
3. How does the change of base formula for logarithms work in differentiation?
4. Can you apply the chain rule to differentiate more complex logarithmic functions?
5. How do logarithmic derivatives relate to exponential functions?

Tip: When differentiating logarithms with any base, converting to natural logs often simplifies the process.