Using all the digits 4, 9, 0, 5, form:

1. Determine the possible last digits for a multiple of 5

A number is a multiple of $5$ if its last digit is $0$ or $5$. The available digits are $4, 9, 0, 5$. So the last digit can be $0$ or $5$.

2. Determine the smallest 4-digit number by arranging the remaining digits

To make the number as small as possible, the first digit must be the smallest non-zero digit available, which is $4$.
If the last digit is $0$, the remaining digits are $5$ and $9$. The smallest arrangement is $4590$.
If the last digit is $5$, the remaining digits are $0$ and $9$. The smallest arrangement is $4095$.
Comparing the two possibilities: $4095 < 4590$.

1. Find the largest possible 4-digit number less than 5000 using the given digits.

The number must start with $4$. To make it as large as possible, arrange the remaining digits ($9, 0, 5$) in descending order: $4950$.

2. Find the smallest possible 4-digit number greater than 5000 using the given digits.

The number must start with $5$. To make it as small as possible, arrange the remaining digits ($4, 9, 0$) in ascending order: $5049$.

3. Compare the differences from 5000 to determine which is closer.

Difference for $4950$: $5000 - 4950 = 50$
Difference for $5049$: $5049 - 5000 = 49$
Since $49 < 50$, $5049$ is closer to $5000$.