John in CR said:
In USD $1k high efficiency drive system (motor/controller), $1k of battery (salvaged from an EV car pack), $1k of construction materials. That leaves you with $2k of room for solid light moto specific parts (maybe a used already registered frame as a shortcut), a Cycle Analyst, and cost overruns. Talk to member Bluefang about the engineer approval process down there, since he's been thru it for an electric moto conversion. Bring a bit of frugality to the equation and EVs can be done incredibly cheap and still obtain all your goals except that 60kg weight.
A significant concern could be legal vehicle requirements such as seat height that could make a bike/trike so low something you can't get approved.
A leaning delta trike is fairly straight forward in design that allows a very narrow build (important for aerodynamics), and a simple lean lock mechanism gives you the stationary stability you'll want without needing to put your feet down. Member Willow, also down under, has higher seated delta leaner he designed as a Postie electric replacement, and he might be able to offer some design advice.
Have you build something like that for 5k? I mean not some used bike somehow made to go like rocket and with no guarantee if you stay alive? Velo guys should chime in to get this on the ground.
1k for drive system? Nonsense, there is not only controller and motor. You need wheels, tyres, hubs, chains, sprockets, shocks, steering components, specialty hardware, etc, etc.
1k for battery to go 160km at 110km/h - nonsense, show me one, must be light

1k for materials - maybe, but then he talks about efficiency and all the gear and materials should be at least above average. Not for sub 60kg, not even close.
Oh, and then there is legal stuff, and that will cost.
For the given parameters, not in a million years for 5k.
You list the cost to build a vehicle like Amberwolf's trike