1. **State the problem:** Solve the equation $$\frac{w - 5}{2} = \frac{5}{3}$$ for $w$. 2. **Use the cross-multiplication formula for proportions:** If $$\frac{a}{b} = \frac{c}{d}$$ then $$ad = bc$$. 3. **Apply cross-multiplication:** $$3(w - 5) = 2 \times 5$$ 4. **Simplify the right side:** $$3(w - 5) = 10$$ 5. **Distribute 3 on the left side:** $$3w - 15 = 10$$ 6. **Add 15 to both sides to isolate the term with $w$:** $$3w - 15 + 15 = 10 + 15$$ $$3w = 25$$ 7. **Divide both sides by 3 to solve for $w$:** $$\frac{\cancel{3}w}{\cancel{3}} = \frac{25}{3}$$ $$w = \frac{25}{3}$$ **Final answer:** $$w = \frac{25}{3}$$