Calculus (3rd Edition)

$$f'(3)=\frac{1}{3 \ln 5}.$$
Recall that $(\log_b x)'=\dfrac{1}{(\ln b)x}$ Since $f(x)=\log_5x$, then we have $$f'(x)=\frac{1}{x \ln 5}$$ and hence $$f'(3)=\frac{1}{3 \ln 5}.$$