(i) The direction vector of \(l_1\) is obtained from the points \((0, 1, 5)\) and \((2, -2, 1)\), which is \(\begin{pmatrix} 2 \\ -3 \\ -4 \end{pmatrix}\).

The direction vector of \(l_2\) is \(\begin{pmatrix} 1 \\ 2 \\ 5 \end{pmatrix}\).

Since the direction vectors are not parallel, the lines are not parallel.

Express the general point of \(l_1\) as \((2\lambda, 1 - 3\lambda, 5 - 4\lambda)\) and \(l_2\) as \((7 + \mu, 1 + 2\mu, 1 + 5\mu)\).

Equate at least two pairs of components and solve for \(\lambda\) and \(\mu\). Verify that all three component equations are not satisfied, confirming the lines are skew.

(ii) The direction vector of \(l_2\) is \(\begin{pmatrix} 1 \\ 2 \\ 5 \end{pmatrix}\) and the direction of the \(x\)-axis is \(\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}\).

The scalar product is \(1 \times 1 + 2 \times 0 + 5 \times 0 = 1\).

The magnitudes are \(\sqrt{1^2 + 2^2 + 5^2} = \sqrt{30}\) and \(\sqrt{1^2} = 1\).

The cosine of the angle is \(\frac{1}{\sqrt{30}}\).

The angle is \(\cos^{-1}\left(\frac{1}{\sqrt{30}}\right) \approx 79.5^\circ\) or \(1.39\) radians.