All items are equally likely.
Let $\sigma$ be variance and $\mu$ be the mean.
$ \sigma =\Sigma_{i=1}^n \frac{(x_i - \mu)^2}{n} \\= \Sigma_{i=1}^n \frac{{x_i}^2}{n} - \Sigma_{i=1}^n \frac{2x_i \mu}{n} + \mu^2
\\=\Sigma_{i=1}^n \frac{{x_i}^2}{n} -2\mu^2 + \mu^2
\\=\Sigma_{i=1}^n \frac{{x_i}^2}{n} - \mu^2$
So, $\Sigma_{i=1}^n {{x_i}^2} = (\sigma + \mu^2) n \\= (5^2 + 2500) 100 \\=252500$