Given that the arithmetic mean of x, y and z is 80.
$$Rightarrow$$ $$dfrac{x+y+z}{3} = 80$$ $$Rightarrow$$ $$x+y+z = 240$$  ... (1)
Also,  $$dfrac{x+y+z+v+u}{5} = 75$$ $$Rightarrow$$ $$dfrac{x+y+z+v+u}{5} = 75$$
$$Rightarrow$$ $$x+y+z+v+u = 375$$
Substituting values from equation (1), $$Rightarrow$$ $$v+u = 135$$
It is given that u=(x+y)/2 and v=(y+z)/2. $$Rightarrow$$ $$(x+y)/2+(y+z)/2 = 135$$
$$Rightarrow$$ $$x+2y+z = 270$$
$$Rightarrow$$ $$y = 30$$   (Since $$x+y+z = 240$$) 
Therefore, we can say that $$x+z = 240 - y = 210$$. We are also given that x ≥ z,  Hence, $$x_{min}$$ = 210/2 = 105.