A DOS type partition table can describe an unlimited number of partitions. In sector 0 there is room for the description of 4 partitions (called 'primary'). One of these may be an extended partition; this is a box holding logical partitions, with descriptors found in a linked list of sectors, each preceding the corresponding logical partitions. The four primary partitions, present or not, get numbers 1-4. Logical partitions start numbering from 5.
There are several *fdisk programs around that can be used to access and modify the DOS type partition table. Each has its problems and strengths. You should choose them in the order parted, cfdisk, disk and sfdisk.
Indeed, cfdisk is a beautiful program that has strict requirements on the partition tables it accepts, and produces high quality partition tables. Use it if you can. Fdisk is a buggy program that does fuzzy things - usually it happens to produce reasonable results. Sfdisk is for hackers only.