1. **State the problem:** We are given a table of values for $t$ approaching some integer $a$ from the left side, and corresponding values of $f(t)$. We need to determine the integer $a$ given the limit $\lim_{t \to a^-} f(t)$. 2. **Analyze the table:** The values of $t$ are 4.5150, 4.9750, 4.9975, 4.99975, and 5.0000. These values approach 5 from the left side (since they are less than 5 and getting closer to 5). 3. **Conclusion:** Since $t$ approaches $a$ from the left and the values approach 5, the integer $a$ must be 5. **Final answer:** $a = 5$