I just ran Windows 10's Anniversary Update which has destroyed my partition table (seems like a common problem that I wasn't aware of before running it...)
I had C: for windows, D: for files and a partition for Linux and one EFI partition. Now Linux is gone, D: is gone. Only C: is still there which has none of my important files

With Testdisk I can still access my Linux partition so I'm trying to make backups of some of my files (it's extremely slow). What used to be the D: partition is not accessible through Testdisk.
Quick analysis shows this list:
1 P EFI System [EFI system partition]
2 P MS Reserved [Microsoft reserved partition]
2 P MS Reserved [Microsoft reserved partition]
3 P MS Data [Basic data partition] [Windows]
4 P Unknown [Basic data partition]
5 P Unknown [Linux]
I assume P (primary) is incorrect. Can I simply change the partition type or what am I supposed to do here? I'd really appreciate some help.
Thanks