1. **State the problem:** Solve for $x$ in the equation $\log_6 36 = 5x + 3$. 2. **Recall the logarithm definition:** $\log_a b = c$ means $a^c = b$. 3. **Evaluate the logarithm:** Since $36 = 6^2$, we have $$\log_6 36 = \log_6 6^2 = 2.$$ 4. **Substitute back:** The equation becomes $$2 = 5x + 3.$$ 5. **Isolate $x$:** $$5x = 2 - 3 = -1.$$ 6. **Divide both sides by 5:** $$x = \frac{-1}{5}.$$ 7. **Use \cancel to show division:** $$x = \frac{\cancel{-1}}{\cancel{5}} = -\frac{1}{5}.$$ **Final answer:** $x = -\frac{1}{5}$.