First, calculate \(\Sigma x\) using the mean:

\(\text{Mean} = \frac{\Sigma x}{18} = \frac{58}{9}\)

\(\Sigma x = 18 \times \frac{58}{9} = 116\)

Now, find \(\Sigma (x - 5)\):

\(\Sigma (x - 5) = \Sigma x - 18 \times 5 = 116 - 90 = 26\)

Next, calculate \(\Sigma (x - 5)^2\) using the formula:

\(\Sigma (x - 5)^2 = \Sigma x^2 - 2 \times 5 \times \Sigma x + 18 \times 5^2\)

\(\Sigma (x - 5)^2 = 967 - 2 \times 5 \times 116 + 18 \times 25\)

\(\Sigma (x - 5)^2 = 967 - 1160 + 450 = 257\)