1. **Problem Statement:** Two dice are thrown simultaneously. We need to find the probability that the sum of the numbers on the dice is greater than 5 and less than 8. 2. **Total Possible Outcomes:** Each die has 6 faces, so total outcomes when two dice are thrown is $$6 \times 6 = 36$$. 3. **Favorable Outcomes:** We want sums $$>5$$ and $$<8$$, i.e., sums of 6 or 7. 4. **Sum = 6:** Possible pairs are (1,5), (2,4), (3,3), (4,2), (5,1). Number of outcomes = 5. 5. **Sum = 7:** Possible pairs are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Number of outcomes = 6. 6. **Total favorable outcomes:** $$5 + 6 = 11$$. 7. **Probability formula:** $$P = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{11}{36}$$. 8. **Final answer:** The probability that the sum is greater than 5 and less than 8 is $$\boxed{\frac{11}{36}}$$.