I have never left a Nav V (or any other device) in the cradle of a dormant motorcycle for a protracted period and certainly not for five days. As such, I don't know what state a device 'rests' in whilst the motorcycle is dormant but it should be possible to find out. I suspect it's not fully turned off but simply, asleep.
From your other posts, you seem to have a Twin Cam 1200. I assume that the device's cradle is powered from the dedicated canbus socket up near the oil cooler / underneath the beak? If so, it should - after a reasonably short delay - power off when the ignition is turned off. If your device is not powered this way, how is it powered?
Going from memory, when you turn the bike's ignition off:
1. The device should stay live, the screen illuminated
2. After a short while, say between 30 seconds and two minutes, the screen should display a message that external power has been lost and that the device will shut down in 30 seconds, would you like to turn the device off or leave it on?
Again from memory, my bike displays this message twice. Once when I first turn the bike off, say when I arrive at a fuel station; if I touch the screen to instruct the device to say on, I get the same message again when the canbus power is lost, somewhere around a minute or two later. Do you get these messages? What do you do when you see the messages? If you do not get these messages, what do you see and / or do?
If I allow the bike to run through its 30 seconds to shut down, let the device to go blank and then remove it from the cradle, I think the device will have entered a sleep mode, not turned fully off. By this I mean I can reawaken the device again quite quickly by - from memory - just pushing the power button briefly. I think I do not have to turn the device on, by holding the power button down for a protracted period. What does your device do?
From memory, as I do not have a Nav V to hand, there are some choices as to how the device is to behave when running on its internal battery. Again from memory, these give the owner some choices as to how long the device stays powered for - running on its internal battery - if external power is not present. If my memory is correct and the choice setting are there, what are your choices set to?
In your case, despite what the dealer told you, I don't think it's very clear where the cause of your problem lies. As I said, I don't think I have ever left a GPS device attached to a dormant bike for anything like five days; so I have no way of knowing if it would flatten the bike's battery. Simple logic dictates that it shouldn't, ie Off should mean Off. But if Off actually means asleep, that is something different. If your dormant bike is somehow seeing the device as something (like the clock or an alarm) that needs to be powered - as it is in sleep mode - and / or it is illuminating the Nav V's screen for five days in the process, then indeed it may well flatten the bike's battery. In other words, it is a problem (maybe insurmountable) in that the device sleeps but the bike's canbus system keeps it ticking over in sleep mode.... ie. It's a problem in two parts, both interrelated.
Of course it could be as simple as being nothing at all to do with the GPS device at all but plenty to do with:
1. Your bike's battery being on its way out, unable to hold a charge and flattening itself
2. Something else - other than the navigation device - draining the bike's battery of power
Again, it should be easy to maybe find out via a very crude - and not completely conclusive - test. Turn the bike off, remove it from any battery tender (like an Optimate) and take the device out of its cradle. Leave the bike for five days. Turn the bike on and try start it. Does it start quickly and properly?
No? Well, it's not the navigation device itself that caused the bike's battery to flatten, as it's not been present.
Yes? OK repeat the test with the navigation device in. What happens this time? If the bike fails to start, then - whilst it's not conclusive proof that the Nav V device itself is solely the cause - you'll at least be on the way to finding out what the cause is.
Me? I'd just take the device off the bike when I was not planning on using it for several days, irrespective.