What is the effect of the Load Factor on wing Structures?
https://en.m.wikipedia.org/wiki/Load_factor

As a start for an aircraft the load factor is the ratio of total lift to total Weight

An easy way to imagine this concept is to understand the idea that when the aircraft is flying at high speed during cruise with a small angle of attack the load factor is very close to 1, this corresponds to the first case on the left of the picture here below

Now what is lift, the picture here below is self explanatory, so it is important to understand that the lift is not always an upward vertical force; when the aircraft is under a coordinated bank angle the lift has two components ; horizontal and vertical.



Now to simplify we shall consider the lift to be totally produced by the wings, while in real flight it is the result of the wing, the body, and the tail.

Since the Aircraft is subjected to a load factor of 2 this means the aircraft as a complete body is subjected to a total lift( not vertical) equal to twice the total weight of the Aircraft

The lift produced is therefore: $2\cdot(5000 + 1500)\,\mathrm{kg}\cdot g = 13000\,\mathrm{kg}\cdot g = 128\,\mathrm{kN}$

If we consider we are in the steep banked turn indicated on the right of the picture above:

The weight of the aircraft body without the wings is a downward force on the root of the wings

Also the wings have their own distributed weights, that produces a torque to the root of the wings

Also the distributed fuel in the wings produces a torque to the wings roots

Also each wing is subject to a distributed lift of $\ 6500\,\mathrm{kg}\cdot g = 63.8\,\mathrm{kN}$

The exact computation are difficult because


we don’t know the bare weight of the wing nor the centre of gravity of the wing
we don’t know the distribution of the fuel in the wing, so we don’t know the centre of gravity of the fuel of each wing.


Therefore it is impossible to calculation the shear forces and the torques at the wings roots.

Nevertheless I imagine the main question concerns the relationship between lift and load factor, And here the most important point is to understand that the lift is not always a vertical force