I suspect the output cap (the electrolytic mounted on the banana jack PCB, if your 3005D is like mine) has failed.
I've been working on pimping my 3005D (better displays, output load switch, etc.), and one thing I discovered is that with that cap disconnected, the thing couldn't really regulate at all. (It stayed at something like 55V!)
Your discovery that adding a cap stabilizes it would support the failed output cap theory.