1. Problem: Find the value of $y$ if $5:8::y:32$. 2. This is a proportion problem where two ratios are equal: $\frac{5}{8} = \frac{y}{32}$. 3. To solve for $y$, cross multiply: $$5 \times 32 = 8 \times y$$ 4. Simplify the multiplication: $$160 = 8y$$ 5. Divide both sides by 8 to isolate $y$: $$\frac{160}{\cancel{8}} = \frac{8y}{\cancel{8}}$$ 6. Simplify the division: $$20 = y$$ 7. Therefore, the value of $y$ is $20$. Final answer: $y = 20$