1. Digits available

We have the digits: $\{0,1,3,5,7,9\}$

We need to form five-digit numbers such that:

• the number is greater than $40000$,
• the number is divisible by $5$,
• no repetition of digits is allowed.

2. Condition for divisibility by 5

A number is divisible by $5$ if its last digit is either $0$ or $5$.

So we consider two cases:

• Case 1: last digit $=0$
• Case 2: last digit $=5$

Also, since the number must be greater than $40000$, the first digit must be one of: $5,7,9$ (we cannot use $4$ since it is not available, and $0,1,3$ would make the number less than $40000$).

3. Case 1: Last digit is $0$

Form: $\boxed{\_\ \_\ \_\ \_\ 0}$

The first digit must be chosen from $\{5,7,9\}$, so there are: $3\text{ choices}$

After choosing the first digit, we must fill the middle three places using any $3$ of the remaining $4$ digits.

Number of ways: ${}^{4}P_{3}=4\cdot 3\cdot 2=24$

So total for Case 1: $3\times 24=72$

4. Case 2: Last digit is $5$

Form: $\boxed{\_\ \_\ \_\ \_\ 5}$

Now the first digit must again make the number greater than $40000$. Possible first digits are from $\{7,9\}$.

Why not $5$? Because $5$ is already used in the last place and repetition is not allowed. So first digit choices: $2\text{ choices}$

After fixing the first and last digits, we have $4$ remaining digits, out of which we fill the middle three places: ${}^{4}P_{3}=24$

So total for Case 2: $2\times 24=48$

5. Total count

$72+48=120$

6. Compare with options

The required number is: $\boxed{120}$

So the correct option is: $\boxed{\text{C}}$

7. Comparison with stored answer

Stored correct answer: C

Our derived answer is also C.