I didn't find any problem with the partition table because hda5 starts from 2 and not 1913. The table is correct without any overlaps and dead spaces. Partitions are tightly following each other and should have no problem in operation.
The only screwy bit of it is the extended partition is at the start of the disk with 30Gb, leaving 220Gb space at the back.
To use the remaining space effectively needs a bit of skill because there can be further 3 primary paritions; hda2, hda3 and hda4. However if the partition hda2 is formed after hda7 then no more logical partition is possible.
Therefore the correct way to do it is to tell the partitioning program that hda2 should start from the end of the disk, so should be hda3 and hda4. Whatever space left is therefore a void after hda7 and hda4 so that additional logical partitions from hda8 to hda60 can be created.
I can't advise on vmware partitions as I haven't used them before. However in moving the Linux to another partition it will become unbootable and needed to be rescued. LVM is complicated in that it addresses the root of Fedora by a "Label" and not by the partition number. The Label is generated by the installer. Therefore I am not hopeful, otherwise it is only a matter to amend /boot/grub/menu.lst and /etc/fstab files after migration.
Thus my suggestion is to make may be hda2, hda3, and hda4 at the rear end of the disk to receieve hda5, hda6 and hda7.
The method to move them.
You need to partition hda5 exactly the same size as hda4 and the same partition type. Similarly for hda6 to match hda3 and then hda7 same size as hda2. Then these lines will mirror the 3 across
dd if=/dev/hda5 of=/dev/hda4 bs=32256
dd if=/dev/hda6 of=/dev/hda3 bs=32256
dd if=/dev/hda7 of=/dev/hda2 bs=32256
You can then proceed to make the hda2, 3 & 4 work while still have the original versions.