I now have 5 Roku devices. If I sign up for a premium streaming service, is it supposed to be accessible on all 5 Roku devices or just the one I used to buy it?
I've only ever subscribed to such services (Netflix, Prime, Hulu, Acorn, etc.) directly through the services, not through an intermediary like Roku. In my case, all that is necessary is to install that specific service's Roku channel app. Downloading to one device will add it to your ACCOUNT and thus will add it to the other devices linked to that same account. (Possible exception: some channel apps will require the features and processing power of later Roku models and may not be available for some older units.) It WILL be necessary to link each of your devices to the channel apps, though.
If you subscribe through Roku rather than directly with the channel, I'd expect things to be about the same.