I cannot find the option to convert a CS5 file down to a CS3; do I need to keep a copy of CS3?
You need to do it in steps.
In CS5 you export to IDML. Then open in CS4. Then export to an interchange format file. Then open in CS3 and save.
So yes you need all three versions to get to a CS3 version document - and there you will have lost what is not supported in the 2 versions older application. Not a recommended workflow.