Yes, you can go from 5.3 to 6.0 then to 6.1 > 6.2 and then 6.3. Run everything in your environment through E-Lab to make sure everything is in the support matrix.
During my next scheduled maintenance cycle, I'm planning on upgrading my Brocade switches from 6.1 to a newer/latest release.  I see that 6.4 is out there now but I have a couple of questions...one I think I know the answer, the rest I'm not sure...  The release notes indicate that I need to step-upgrade from 6.1->6.2->6.3->6.4 - there are a lot of sub-versions listed and available out there.  When something says "minimum release 6.1.0a can I assume this means that 6.1.0_8e1 is as high as this?  If my version isn't high enough, will it bark at me?  From the look of things, it appears that upgrading to the latest release of each in-between version will be sufficient.  The second question is about the items removed from the web tools - I have a very static environment and till now the web tools have been sufficient for what I need to do (i.e. set up zoning) - in the release notes it says something about functions moving to DCFM which I understand is free...am I going to need to install that in order to do simple aliases and zoning?  The release notes just aren't that clear to me.  6.4 looks new - anyone have any "oh no don't upgrade to THAT" comments?  Dan
Brocade Upgrade