You can not account or skewness in the mean-variance framework as skewness is the third central moment.
Thus what I would do is
- formulate the skewness in terms of the asset returns. I.e. for each time-step you have
$$
r_t = \sum_{i=1}^5 w_i r^i_t,
$$
where $r_t^i$ is the return of asset $i$ at time $t$, $w_i$ is the weight and $r_t$ the portfolio return at $t$.
Then you can use the empirical estimator of skewness:
$$
skew = \frac{ 1/T \sum_{t=1}^T (r_t-\mu)^3}{ \sigma^3},
$$
where you need the portfolio variance
$$
\sigma^2 = w \Sigma w
$$
and the expected value
$$
\mu = 1/T \sum_{t=1}^T r_t,
$$
where the above is the sample estimator and
$$
\mu = \sum_{i=1}^5 w_i \mu_i
$$
is the expression in terms of individual expectations.
Then you can use this skewness above, $\sigma$ and $\mu$ to define the problem. E.g.
$$
\mu - \lambda \sigma^2 \rightarrow Max
$$
under the constraint $skew \ge x$ for some desired level $x$.
Or you use the definition of Cornish-Fisher-VaR in the constraint.