Short Answer: No you cannot run Adobe CS5 on a Linux machine.
Longer Answer: You could, however, attempt to virtualize a Windows instance on the Ubuntu machine using such things as VMWare Player, VirtualBox, KVM and others. I have attempted to run Photoshop elements in a virtual machine and the experience was... unfavorable. CS5 would likely be even worse, unless you have a juggernaut of a PC powered by a blackhole and can dedicate many gigabytes and many cores to the VM.
You will likely want to consider dual booting with just enough space on the Windows partition to do what you want. That would be cumbersome, I'm sure. You'll likely need some shared storage, like an external NFTS drive, to put your files on so that you can see them in Windows, and then also see them in Linux. Note: Windows does not see Linux filesystems without the aid of third party software.
Another option is to do what I've done, and that is use Linux as your main OS (Fedora 14 for me) and then have a Windows machine on the side that you use for other things such as Photoshop. Actually, I have a spare laptop hard drive that I installed Vista on. On weekends I swap drives out to do some gaming ala Steam. To my right is a Vista workstation that I use for Photoshop and as a test PC. Certainly not what most people are willing to put up with, but I'm a SysAdmin. You get numbed to crazy things after a while.
Any way you go, you won't have the most seamless experience unless / until Adobe makes a native Linux version of their products. We can dream, can't we? Or you could just get a Mac and have the joy of Adobe products along with a gloat-worthy notation of running a UNIX03 certified OS (depending on the exact OS X version, of course).
Edit: If learning Linux is your goal, perhaps you can do things the other way around. Run Windows, but keep Linux in a VM and migrate things into it. First, it makes backups a little easier since you can simply
robocopy the virtual machine folder to a backup drive. Second, you have the safety of Windows if things get too scary in Linux (although, that could also be a downside since when things got scary for me I had to fix it or I had no PC to work with. I learned a lot). Finally, you've got Windows to run CS5 on.
Most Virtual Machine programs allow you to run the VM in full screen mode so you'd never know you weren't on a physical machine.