Can it be done?
The short answer is, yes! However, it's not as simple as clicking a few buttons. That being said, there are tools available to help you out with this process. I'll mention them below. Keep in mind that one of the biggest things you need to consider is your sites template. It's highly likely that you will need to have a new Joomla 2.5 (or just use the inbuilt templates initially) ready when you migrate your site.
Again, as has been mentioned before on this site, Joomla 1.5.x to Joomla 2.5 is a MIGRATION, not an upgrade. So here goes...
Things you'll need:
If you need any more help with this process, be sure to drop into the following Joomla forum section