1. **State the problem:** Solve for $y$ in terms of $r$ and $t$ in the proportion $$\frac{y - t}{3} = \frac{y - r}{5}.$$\n\n2. **Use cross-multiplication:** Multiply both sides by the denominators 3 and 5 to eliminate the fractions:\n$$5(y - t) = 3(y - r).$$\n\n3. **Distribute:**\n$$5y - 5t = 3y - 3r.$$\n\n4. **Group like terms:** Move all terms involving $y$ to one side and constants to the other:\n$$5y - 3y = -3r + 5t.$$\n\n5. **Simplify:**\n$$2y = 5t - 3r.$$\n\n6. **Solve for $y$ by dividing both sides by 2:**\n$$y = \frac{5t - 3r}{\cancel{2}} \cancel{\times \frac{1}{2}} = \frac{5t - 3r}{2}.$$\n\n**Final answer:** $$y = \frac{5t - 3r}{2}.$$\n\nThis means the answer choice $y = 5t - 3r$ is incorrect because it misses dividing by 2.