Answer
$$ f'(3)=\frac{1}{3 \ln 5}.$$
Work Step by Step
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
$$ f'(3)=\frac{1}{3 \ln 5}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 50
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