Answer
$-\dfrac{1}{5}$
Work Step by Step
$\because y=\log_a x \text{ is equivalent to } x= a^y$
$\therefore 5x+3 = \log_6 36 \text{ is equivalent to } 36=6^{5x+3}$
With $36=6^2$, solve the equation above using the rule $a^m=a^n\implies m=n$ to obtain:
\begin{align*}
36&=6^{5x+3}\\\\
6^2&=6^{5x+3}\\\\
2&=5x+3\\\\
2-3&=5x\\\\
-1&=5x\\\\
\frac{-1}{5}&=\frac{5x}{5}\\\\
-\frac{1}{5}&=x
\end{align*}
