(i) To find the probability of obtaining a total score of 5, we list all possible combinations of scores on the three dice that sum to 5:

• (1, 1, 3)
• (1, 2, 2)
• (1, 3, 1)
• (2, 1, 2)
• (2, 2, 1)
• (3, 1, 1)

There are 6 combinations. Since each die has 6 faces, the total number of possible outcomes when throwing three dice is \(6^3 = 216\). Thus, the probability is \(\frac{6}{216} = \frac{1}{36}\).

(ii) To find the probability of obtaining a total score of 7, we list all possible combinations of scores on the three dice that sum to 7:

• (1, 2, 4) and permutations: 6 combinations
• (1, 3, 3) and permutations: 3 combinations
• (2, 2, 3) and permutations: 3 combinations
• (1, 1, 5) and permutations: 3 combinations

There are 15 combinations. Thus, the probability is \(\frac{15}{216} = \frac{5}{72}\).