Try reassociating the INDD files with CS5.5 by right clicking an INDD file and choosing open with. Browse to the EXE for InDesign CS5.5. This may or may not work.
Installing out of order is not a very good idea. You may well be better off uninstalling everything and reinstalling in order.
Definitely better off uninstalling and reinstalling in the correct order.
And if you don't actually want InDesign CS3 (but I see no reason not to), do a custom install and only install those things that will be useful to you.
Sorted. Clicked uninstall on Design 3 Suite and it allowed me to just checkbox InDesign CS3 application in isolation. Thanks for the help.
Don't be surprised if you find things don't work as expected down the road -- it's a frequent problem when old versions are removed after installing new ones. In your case, it's harder to predict since the old version was installed last, but there's a good chance some common files were overwritten by CS3 and CS5.5 won't like the older versions.