1. **State the problem:** Solve the equation $$\frac{8}{14} = \frac{5}{x}$$ for $x$. 2. **Use the cross-multiplication formula:** For two fractions equal to each other, $$\frac{a}{b} = \frac{c}{d}$$, cross-multiply to get $$a \times d = b \times c$$. 3. **Apply cross-multiplication:** $$8 \times x = 14 \times 5$$ 4. **Simplify the right side:** $$8x = 70$$ 5. **Solve for $x$ by dividing both sides by 8:** $$x = \frac{70}{8}$$ 6. **Simplify the fraction by dividing numerator and denominator by 2:** $$x = \frac{\cancel{70}^{35}}{\cancel{8}^{4}}$$ 7. **Final answer:** $$x = \frac{35}{4}$$