Changing from 6 (or 7?) down to 5 speeds may or may not be straightforward. We need more details to help you with that. I would recommend keeping the original freewheel or if necessary changing to one with the same number of cogs and same spacing, to keep life simple. Next you mention preserving the original "cassette" (freewheel?), which is exactly what I would do if it is in good working order or at least rebuildable.
A new chain is no problem, assuming the cogs are not significantly worn. Close up photos will help us to make that assessment.
We can then advise you on your options.
If it's the one I'm thinking of, the Gran Sport is a bit archaic in appearance and function for your application, but it might work, depending on the max cog, swing, and chain wrap you need. I'd recommend you consider keeping the original derailleur or look at other options if you have a reason to change the derailleur.