Select installation preference and select "Download updates while installing Ubuntu", (optional), and Select "Install third-party software ...", (optional), click "Continue".
If asked about unmounting partitions that are in use, select Yes, click "Continue".
Do not use Advanced feature disk encryption for this install method. (See Note 4 at bottom).
At "Installation type" select "Something else", click "Continue".
Under Device for boot loader installation select the target drive.
Select partition sdx4 and click change, select use as Ext4, select “format this partition”, and Mount point = "/" then OK.
If asked to Write previous changes... click Continue.
Select partition sdx5 and click change, select use as Ext4, select format this partition, and Mount point = "/home" then OK. (optional).
Click Install now.
Confirm partitions to be formatted if asked, click continue.
Select your location. click "Continue".
Insert your name, computer name, username, password and select if you want to log in automatically or require a password. - Click "Continue".
Wait until install is complete.
Turn off computer and re-plug in the HDD.
Replace the computer's cover.
Note 1: Problems
If there are any problems booting, first try re-installing GRUB:
sudo mount /dev/sdx3 /mnt sudo grub-install --boot-directory=/mnt/boot /dev/sdx
Next, if there is an efi entry in fstab, # it out.
Note 2: Hard drive removal.
You may omit disabling the hard drive in BIOS boot if after partitioning you choose to install grub to the root of the USB drive you are installing Ubuntu to, (ie sdx not sdx1). Be cautious, many people have overwritten the HDD MBR as default location for boot loader is sda, any items in the internal drive's grub will be added to the USB's grub. You may do an update-grub later. If you leave the HDD plugged in with UEFI install, fstab may use the HDD's UUID for /boot/efi. In this case # or delete the /boot/efi.UUID line in fstab.
Note 3: Apple compatibility.
If you own an Apple computer make this partition FAT32.