1. **State the problem:** Solve for $x$ in the equation $5(-3 + x) = 35$. 2. **Use the distributive property:** Multiply 5 by each term inside the parentheses. $$5 \times (-3) + 5 \times x = 35$$ which simplifies to $$-15 + 5x = 35$$ 3. **Isolate the term with $x$:** Add 15 to both sides to move the constant term. $$-15 + 5x + 15 = 35 + 15$$ which simplifies to $$5x = 50$$ 4. **Solve for $x$ by dividing both sides by 5:** $$\frac{\cancel{5}x}{\cancel{5}} = \frac{50}{5}$$ which simplifies to $$x = 10$$ 5. **Final answer:** $$\boxed{10}$$