1. Stating the problem: We need to find the value of $n$ in the equation $$\frac{10n}{3} - 1.5 = 14.5$$. 2. Add $1.5$ to both sides of the equation to isolate the term with $n$: $$\frac{10n}{3} = 14.5 + 1.5 = 16$$. 3. Multiply both sides by $3$ to eliminate the denominator: $$10n = 16 \times 3 = 48$$. 4. Divide both sides by $10$ to solve for $n$: $$n = \frac{48}{10} = 4.8$$. 5. Final answer: $n = 4.8$.