There might be a way to get linux on the axim. I have been searching for a few weeks and the best that I can come up with is using an X86 emulator to run DSL or Pupply linux. I was trying to get this to work on an hp ppc of mine but it looks like the compiled emulators may work on the axim's cpu and not the hp. So I have yet to test this. I do know that the same emulators have been ported to the Sony PSP. Users of this system have been able to run Windows 3.1, Windows 95, Puppy and DSL. This is the link to the PPC X86 emulators
Mamaich home page. There is another option offered here
Handhelds.org - Linux on Dell Axim X5. That option is to run a port of linux within the axim's default O/S. It only seems to run for about 15 min. before forcing the user to hard reset the device.