|I assume, the 4 already existing partitions are all of type primary.|
That's a problem, because the MBR (Master Boot Record) can only have 4 partition entries.
To add more partitions, one of these 4 partitions must be of the type "Extended Partition".
In an extended partition, you can create other logical partitions, at maximum 24 logical partitions.
So you have to delete one of the primary partitions and then create an extended partition, where you can add additional partitions you need.
But keep in mind, when deleting a partition, all data on this partition is lost.
So you need to backup or image this partition before deleting it.
The original poster should always write the last response !!!
Let us know, if the problem is solved !!!