1. The problem states: If $a * b$ means $\frac{1}{4}(a - b)$, find the value of $5 * 3$. 2. The operation $*$ is defined as $a * b = \frac{1}{4}(a - b)$. 3. Substitute $a = 5$ and $b = 3$ into the expression: $$5 * 3 = \frac{1}{4}(5 - 3)$$ 4. Simplify inside the parentheses: $$5 - 3 = 2$$ 5. Multiply by $\frac{1}{4}$: $$\frac{1}{4} \times 2 = \frac{2}{4} = \frac{1}{2}$$ 6. Therefore, the value of $5 * 3$ is $\frac{1}{2}$.