Weird partition table

I was given a hard disk to repair/extract data from. This hard drive was once the hard drive of a computer that had windows and linux installed (using grub to change between two). Booting from the hard drive is not possible anymore. When connected to linux, 4 partitions are found (/dev/sdb[1256]), but only /dev/sdb1 can be read. /dev/sdb1 is the grub-partition, while /dev/sdb5 was identified as swap-partition by blkid (it might have been another program, i'll check that). Mounting the partitions 2 and 6 gives errors, var/log/syslog says something about a bad superblock.
Still, the most irritating result gives fdisk -l, which prints the partition table AFAIK.

Device    Start    End        Type
/dev/sdb1     2048  19531775  83 linux
/dev/sdb2 19533822 625141759   5 extended
/dev/sdb5 19533824  36304895  82 linux swap 
/dev/sdb6 36306944 625141759  83 linux

(1 sector equals 512 byte, some of the output was removed by me. I will add it if needed)

If I undmerstand correctly, something is wrong with the partition table. Somehow partition 2 is at the same location as partitions 5 and 6, which might explain the mounting-errors. (I will ask which OS really was used on this hard drive).

Now, there are important files on this hard drive. How do I get these files from the hard drive or (better) alter the hard drive so linux can mount all partitions. My first thought was to make a backup with dd and then let a fsck run on /dev/sdb (You might see I am no expert at this), although I have my doubts.

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