It's the four partitions that are the problem; there's currently no space for Ubiquity to put an extended partition since four logical partitions is the maximum. If there is one of the partitions that is not required then you can delete it and let Ubuiquity make its extended partition. (you can then have many more partitions inside the extended partition).
We need to know what the partitions are currently being used for so that we can advise you on which is the best way to go. Presumably Win7 is your main partition, however it may just be a Microsoft bootloader. The recovery partition is the Windows recovery, which can be used to re-install Windows from scratch if you have to. It's probably a good idea to make the boot DVD's as well, rather than just relying on the recovery partition. HP_tools and System could be anything - but System could be your real Windows partition.
If system partition is indeed the largest and contains the real Windows system, I think I would backup the data on it and delete it. You could then use that space for an extended partition which could contain Windows and the Ubuntu root and swap partitions. Backing up your data at this point would be a very good idea, as is making the Windows install disks - there will be a HP Utility for doing so. After you make the Windows boot disk, make quite sure there are no errors and that you can boot off it.
So that we can help you further, please boot of the Ubuntu LiveCD or LiveUSB and select "try Ubuntu". Next open a terminal windows with ctrlaltt and type
sudo fdisk -l
and past the results from it into your question.
Thanks, that gives us some idea. It looks like:
sda1 hpfs 407551 194MB 208MiB
sda2 hpfs 946182143 451GB 484445MiB
sda3 hpfs 29968383 14GB 15343MiB
sda4FAT32 210991 100Mb 108MiB
It seems that the main partition is /dev/sda2, 450Gb
After backing up and making sure that you have made the Windows installation disks correctly, you could try deleting /dev/sda2 and make and extended partition in its place. You can then make three partitions inside the extended partition: Windows partition, ext4 Linux partition, and a Linux swap partition at least equal to your RAM size.
The problem may be that Windows won't install to a logical partition easily, however a google search finds instructions for this so it should be possible to do so. This might be a little complicated for the Windows installation, so there are a few alternatives:
A Wubi install of Ubuntu uses a Virtual Ubuntu boot disk inside of Windows. It's a good way of using Ubuntu without changing your Windows or the partitions at all. https://wiki.ubuntu.com/WubiGuide
An alternative would be to remove the Windows Bootloader on /dev/sda1 as well since installing Ubuntu will also install the grub bootloader, so it is really redundant. The procedure would be as follows:
- Backup all important data in the Windows installation and make sure that you can access recovery options for Windows such as the OEM installation partition
- On the Windows main partition run chkdsk and defrag the drive
- Delete the Windows bootloader partition
- Resize the main Windows partition to make room for the extended partition - size is up to you (maybe 50/50?)
- Create the extended partition in the space left by resizing Windows.
- Create two partitions inside the extended partition: 1 swap partition of at least the size of your RAM, and the rest as and ext4 partition for Windows.
- Install Ubuntu in the new ext4 partition. After install both Ubuntu and Windows should be accessible.