Step 1 — Find the sum: $\sum x_i = 5\times4=20$. Known three: $3+4+4=11$. So $x_4+x_5=9$.

Step 2 — Find sum of squares: Variance $=\frac{\sum x_i^2}{n}-\bar{x}^2 \Rightarrow \frac{\sum x_i^2}{5}-16=5.2 \Rightarrow \sum x_i^2=106$.

Known: $3^2+4^2+4^2=9+16+16=41$. So $x_4^2+x_5^2=65$.

Step 3 — Solve: $x_4+x_5=9$ and $x_4^2+x_5^2=65$.

$(x_4+x_5)^2=81 \Rightarrow 2x_4x_5=81-65=16 \Rightarrow x_4x_5=8$.

$(x_4-x_5)^2=(x_4+x_5)^2-4x_4x_5=81-32=49$

$|x_4-x_5|=\mathbf{7}$