Use all the digits 4, 5, 6, 8 to form the greatest number between 5 000 and 6 000. Ans: ___

1. Determine the thousands digit based on the given range

The number must be between $5000$ and $6000$. Therefore, the thousands digit must be $5$.

2. Arrange the remaining digits to form the greatest possible number

The remaining digits are $4$, $6$, and $8$. To form the greatest number, arrange these digits in descending order: $8$, $6$, $4$. The number is $5864$.