Answer
$\{log_54 \}$
Work Step by Step
Step 1. Let $u=5^x$, we have $u^2+3u-28=0$ or $(u+7)(u-4)=0$
Step 2. For $u=-7$, we have $5^x=-7$, no solution.
Step 3. For $u=4$, we have $5^x=4$, thus $x=log_54$
Step 4. Write the answers in set form $\{log_54 \}$