Find the Min Value of R in a Zener-Transistor Regulator
WOW. It's teachers like this that make the old adage...

"People who can, DO. People who can't, TEACH!" 

In truth the answer to "Find the minimum acceptable value for R and the tension in the zener diode so that the Vout (Regulated) is equal to 5 V." is ...

"You did not give me enough information to calculate that."

You have no way to tell from this information what the zener current needs to be so it produces the 5.6V voltage you need to get 5V at the output. 

You can NOT calculate that current from the wattage of the ZENER. That value is just how far you can over-stress it before it melts. At that current the ZENER will not be giving you anywhere close to 5.6V even when cold, and it will not stay cold for long at max current.

EDIT

The answer given is 100R... lets look at that.

At 12 + 25% Rail and the diode at 5.6V that's nominally 526.4mW on the diode, so you are already out of spec.

For a typical 5.6V 500mW zener 1N5232, the junction will be close to 175C and Vz will 5.7% higher at 5.92V...

The spec for said diode calls for 20mA to regulate at 5.6V, not 100mA.

Even with that number though, the output will only be at 5V under a very specific set of conditions. That is, almost never.