Hi Glesica,
You can use this BJT-Boosted Zener Voltage Regulator as a reference. If operational amplifier is allowed, try this
Bootstrapped-Reference Voltage Regulator.
In both circuits the DC input voltage (Vdc) can be increased to 14 V. You can keep the value of the ripple voltage (Vripple) or you may change it to, let's say, 1.5 V. This way the total input voltage falls within 12 to 16 V.
The output voltage is ≈ 5 V for both circuits.
To satisfy the remaining "additional requirement"
add an LED in series with a 1 kΩ resistor and connect it across the input voltage (top of Vripple and ground). The value of the resistor and the size of LED depend on the desired brightness.
The Zener diode and BJT in both circuits are generic components, just find the corresponding real parts.
These circuits demonstrate how voltage can be regulated, primarily, using Zener diode and BJT. To be able to focus on the roles of Zener diode and BJT in regulation, the circuits don't have capacitors. This is not a problem because the input voltage and the load are both simple. For real-world applications, input and output capacitors should be installed.
Finally, as both circuits were created to be simple like your stipulation. No overload/short-circuit protection is included in the design. Thus, use it for low-current applications and avoid employing it in circuits where overloading is more likely to occur.
Best regards,
G. Goodwin