This will work: this looks very much like what I do with my own laptop (the only differences are that I don't have a DATA partition and that sizes are different). I now create all my Ubuntu partitions within the extended partition and GRUB2 can start Ubuntu just fine in that configuration.

Please note the following however. In the past, I have used other custom bootloaders that would simply change the active partition dynamically during boot. This would not work in your case as the active partition must be a primary partition. This is probably not a problem as you will likely use GRUB2 to manage your multibooting.

The Ubuntu installer has an option to automatically reduce your Windows partitions and install alongside. If you want more control, you could indeed use Gparted to prepare your partitioning scheme. I believe it's also possible to manually resize your partitions in the Ubuntu installer, but it may feel a bit trickier there: Gparted sounds like a good choice to really see what you're doing. You will then need to select the last option in the installer to manually assign your partitions ("/", "/home" and "swap", plus the Windows partitions if you want to access them, just make sure not to format them!).

On a personal note, I still prefer to shrink my NTFS partitions directly from Windows (inside the Disk Management console or using the DISKPART utility and its SHRINK command), but it hardly seems to matter nowadays.