There is no 5th gen Classic. Classic is the (original) naming for 6G and later. However, these days people seem to mix up things and label all kinds of things as "Classic". Ipod 5G = Ipod Video.
Yes - I (and others) use 'Classic' to distinguish the larger click wheel iPods from the multi Gen nano and Touch models. But technically (and correctly, I suppose), the 5th Gen is the "iPod with Video" (even though it is not the only model that can display videos).
My understanding is that as far as installing and using Rockbox is concerned, the 5th Gen with Video 30 and 60GB models, and the 5th Gen Enhanced 30 and 80GB models are all the same.