LED light glows when switched off
The way you have drawn the circuit is correct for an ungrounded circuit. However if that is your real configuration, slight illumination on lamp 5 is simply impossible.  There is no current path which would make this possible, unless through the grounds.  

That tells me most likely, your drawing does not reflect reality. Inspect more closely. 

You draw grounds like an electronics guy, just stick the symbol there and "armwave" it, but grounding cannot be armwaved.  It is a very big deal. Since the source is not grounded, grounds should not be interconnected amongst the new things you have added: This creates an "island of grounds" (see what I say here): Now touching a switch plate cover screw can kill you. 

Grounds must start at the physical earth, go via the grounding electrode system to the panel, then from the panel to each grounded point in turn. Retrofitting is allowed, so the grounds don't need to follow the same route as the conductors, but grounding must spread from the panel. No islands.  All that said...

....I really don't see how grounds can have anything to do with it, unless you have done something really dumb like bootleg grounds off neutral, or several of your LED lights have neutral-ground faults and they're wired backward or something.  I assume you are checking for that and fixing it. 

Anyway, look closer at your wiring and I believe you will find there's a mismatch between the drawing and what you actually have.  If you want to shoot some pix of the junction boxes, particularly the box where the two subcircuits diverge, we'd be happy to have a look.