Use all the digits 0, 4, 5, 9 to form

1. Identify the condition for the number to be a multiple of 5

For a number to be a multiple of $5$, its last digit must be $0$ or $5$.

2. Determine the largest possible arrangement of the remaining digits

To form the largest number, we must place the largest available digits in the highest place values.

• If the last digit is $0$, the remaining digits are $4, 5, 9$. Arranging them in descending order gives $9540$.
• If the last digit is $5$, the remaining digits are $0, 4, 9$. Arranging them in descending order gives $9405$.
  Comparing the two, $9540 > 9405$.

1. Identify the largest possible number starting with 4 and the smallest possible number starting with 5

The number just below $5000$ must start with $4$ and be as large as possible: $4950$.
The number just above $5000$ must start with $5$ and be as small as possible: $5049$.

2. Calculate the difference between each candidate and 5000 to find the closest

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