(i) To form a number between 5000 and 6000, the first digit must be 5. The remaining digits can be chosen from 1, 2, 3, 4, and 6 without repetition. There are 5 choices for the second digit, 4 choices for the third digit, and 3 choices for the fourth digit. Therefore, the total number of numbers is:

\(1 \times 5 \times 4 \times 3 = 60\)

(ii) If repeated digits are allowed, the first digit is still 5. Each of the remaining three digits can be any of the 6 digits (1, 2, 3, 4, 5, 6). Therefore, the total number of numbers is:

\(1 \times 6^3 = 216\)