It must be greater than $5000$

There are $7$ digits. The thousands digit can be any of the digits $6,8$ and $9$ . There are $3$ possibilities. The hundred’s digit can be any of the remaninng $6$ digit’s. There are $6$ possibilities. The ten’s digit can be any of the remaining $5$ digits. There are $5$ possibilities. The unit’s digit can be any of the $4$ remaining digits. There are $4$ possibilities. Hence, we can form $(3)(6)(5)(4)=360~integers$