3 Phase, 5 Wires Power Supply

It sounds pretty good from here.

Certainly. A very common system--a grounded conductor (the neutral) to carry the unbalanced currents from L1, L2, and L3, and a grounding conductor, used as a safety ground, connected to various things including enclosures.

Now, if you want to be confused, consider the mining industry, with 6 wires--adding the ground check conductor (aka as pilot or monitor wire). It is used to check for continuity of the grounding conductor to the frame of mining machinery.

It does exist. So what is the issue next?

Yep, pretty common here, L1 L2 L3 N PE

Yes! It is called the TN-S system in IEC 60364.

We use this in Oz to get both three phase 440v ( L1, L2, L3, ) and 240v single phase L1, N for some of the outlets and then L2, N for some more with one phase reserved for lighting L3, N in this example. That is to say 440v between phases and 240v between phase and N.

This can cause an imbalance between the phases but as there is no standard either imposed or by convention the rest of the houses in the street will likely as not help to balance the load.