Hi, I'll keep this simple.
5000nm range with full fuel and payload.
Minimum 250kt cruise (ideally closer to 350kts).
Maximum of 20 imperial gallons per hour (440 gallon tank, 400 for flight with 40 gallon reserve).
500kg payload (4 passengers + safety equipment).
Is this possible or not?
The only aircraft that seems to fit is the Scaled Composites Firebird which has a longer range (8000nm) but at a slower speed (200kt) and it has a higher payload capacity (560kg).
Also, I really like the way it looks.