PC partitions can be set up in 2 different ways.

1) As a primary partition, or a "Real" partition. You can only have 4 primary partitions on a hard drive
2) As an "extended" or "logical" partition. This is basically a partition inside a "Real" partition. You can have MANY logical partitions.. more than a dozen. But all of these extended partitions are stored inside a "Real" partition.

In Linux, primary partitions are identified by /dev/devicenameX , where X = 1 through 4
The extended partition names begin at X = 5

So my guess is that your Disk director created partition table looks like this:

sda1 (Primary, FAT/FAT32)
sda2 (Primary, NTFS most likely your "C:" drive)
sda3 (placeholder for extended partition, not a "Real" partition)
and inside sda3:

sda5 (Extended, NTFS, most likely your "E:" drive)

I would not trust the gpart generated information because it looks incorrect. For some reason it saw your "E:" drive as a primary partition and not an extended one. This explains the gap in the last sector of partition #2 and the first sector of partition #3

Chances are that your "Disk Director" has already fixed your partition table correctly, but if you wish to use a different program to try and recover your partition table, I would try "TESTDISK" and not gpart.

Ironically, you can get a version of TESTDISK from the bootable "Gparted" livecd. Just Right-Click on an empty part of the desktop and then choose TESTDISK from the menu. Another option is to burn a copy of the ULTIMATE BOOT CD. I am pretty sure that it contains TESTDISK.

But I would not use gpart to WRITE out a new partition table because the information looks inconsistent to me.

Good Luck.