I believe you can just go Start->Settings->System->System Information to find out what ROM version you currently have, but I don't have that model in front of me to verify it at the moment.
As to upgrading to WM5, most software from WM2003SE will run flawlessly, but there are plenty of exceptions. Thus, after you reinstall all of the software (remember, updating the ROM results in the loss of all of your files and programs, so back it all up in advance) you may have to do a little trial and error to see what fails. If/when you come across one that doesn't work quite right check with the manufacturer for updates. That is, unfortunately, the only method.
I have an iPaq hx2755. I have downloaded the ROM update and other updates. One of the ROM update requirements is to be updating a ROM update of a certain version. How do I check the ROM version on my HP iPaq hx2755? Also, I am thinking of upgrading from Windows Mobile 2003 SE to Windows Mobile 5.0. If I upgrade will I need new programs?