1. **State the problem:** Solve for $x$ in the equation $5x + 3 = 13$. 2. **Write the equation:** $$5x + 3 = 13$$ 3. **Isolate the term with $x$:** Subtract 3 from both sides: $$5x + \cancel{3} - \cancel{3} = 13 - 3$$ $$5x = 10$$ 4. **Solve for $x$ by dividing both sides by 5:** $$\frac{5x}{\cancel{5}} = \frac{10}{\cancel{5}}$$ $$x = 2$$ 5. **Final answer:** $$x = 2$$ This means that when $x$ is 2, the equation $5x + 3 = 13$ holds true.