Can You Design a Diode Circuit to Turn On at 5V and Off at 15V?

[sadf]

Homework Statement

Given an input range of voltages (for example, 5-15V), design a circuit using resistors and diodes (and voltage sources) to turn on at input = 5V and turn off at input = 15V. (I chose 5 and 15 arbitrarily).

Homework Equations

The Attempt at a Solution

I am able to get it to turn on at 5V (I would just put about 7 of the standard 0.7V threshold diodes in series), but my understanding is that the current will skyrocket at 5V and then plateau at a voltage slightly higher than 5. I don't know how to get it to continue rising until 15V and then stop there...

 

[Delphi51]

Welcome to PF, sadf!

I thought I had an idea, then realized it was wrong.
I now think it is impossible to do this without a transistor.