Minimum possible value of x

Given average of $x, y, z$ is 80: $x + y + z = 240$

Average of $x, y, z, u, v$ is 75: $x + y + z + u + v = 375$ Since $x + y + z = 240$, we have $u + v = 375 - 240 = 135$.

Given $u = \frac{x+y}{2}$ and $v = \frac{y+z}{2}$: $u + v = \frac{x + 2y + z}{2} = 135 \implies x + 2y + z = 270$

Subtracting $x + y + z = 240$ gives: $y = 30$

Then $x + z = 240 - 30 = 210$. Since $x \ge z$, to minimize $x$, $z$ should be as large as possible. Since $x \ge z$, maximum $z = 105$ (when $x = z = 105$).

Therefore, the minimum possible value of $x$ is 105.