I have been able to create a dual boot with Ubuntu 15.04 and Windows 10.
It takes some effort but it is doable. I will also have to say I am not an expert so there might be some things missing or I might have used some wrong terminology. If you have any remarks that can add to this answer please feel free to do so.

This is an explanation of how to install Windows 10 after Ubuntu 15.04 has been installed.

Make a backup of all your data

I did not lose any information but it is better to be safe then sorry.

Create bootable flash drives

Ubuntu

I already had a bootable flash drive with Ubuntu 15.04.
If you still need to do this you can find more info here:
https://help.ubuntu.com/community/Installation/FromUSBStick

Windows

To create a bootable flash drive with Windows 10 it takes a bit more effort.
First you will need to download a Windows 10 ISO file. Next you have to mount the ISO file (I used Furious ISO Mount) and copy all the files to the flash drive.

MAKE SURE THE FLASH DRIVE IS FORMATTED AS NFTS. For this you can use gparted.

Set the correct boot sequence in the bios

This is different for every pc. When you are not sure how to get into the bios: just Google: bios boot sequence computer brand or type. You will surely find a forum or a manual that will explain it for your particular system.
On a HP Pavilion this is Esc. :)

Boot the Ubunu 15.04 flash drive

Once booted you can use trial, you do not have to install. We will run Ubuntu from the flash drive. Now the real fun begins. I hope you have done the first step and made a backup. If you did not and you are not sure what you are doing, go back and make a backup.

Create a new partition for Windows 10

You can use gparted to divide your harddrive into multiple partitions.
Right-click on your harddrive and click Resize/move and set the new size for your Ubuntu partition. The rest will go into the new partition you can use for Windows 10.

How you divide the harddisk space is all up to you but keep in mind that windows will take a lot more space than Ubuntu.

The shrinking of the Ubuntu partition might take a while so it is time to get a cup of coffee.

Format

Right-click on the new partition and this time select Format to NFTS.

Set flag

Right-click one more time on the new partition and set the flag to boot.

Set label

This is not mandatory but if you like to keep this organised it is nice to give your partitions a name. Right click on each partition you would like to rename and set the label.

Now you are all set and done to install Windows 10.

Install Windows 10#

Turn off the computer, remove the Ubuntu flash drive and insert the Windows_10 bootable flash drive. Run the installation process. Be sure you install it on the right partition. (Are you still sure you didn't need that backup?)

Reinstall Grub

After installing Windows you will notice that the computer automatically boots into Windows 10. But we wanted to have dual boot. For this we will need to do one more step. We will have to reinstall Grub.
I have found a great link that helped me to do this:
http://www.howtogeek.com/howto/ubuntu/reinstall-ubuntu-grub-bootloader-after-windows-wipes-it-out/

Now you should be all set and done with your brand new Ubuntu 15.04 and Windows Dual boot machine. Awesome.

From this point I would like to thank everyone that helped me to figure this out.