1. **State the problem:** Solve the inequality $5x > 15$. 2. **Formula and rules:** To solve inequalities, we isolate the variable on one side. When dividing or multiplying both sides by a positive number, the inequality direction remains the same. 3. **Isolate $x$:** Divide both sides by 5: $$\frac{5x}{\cancel{5}} > \frac{15}{\cancel{5}}$$ 4. **Simplify:** $$x > 3$$ 5. **Interpretation:** The solution is all values of $x$ greater than 3. **Final answer:** $x > 3$