What follows is a discrete dividend version of my answer in
this post:
When the stock pays dividends it is not true that the deflated stock price
$$
e^{-\int_0^tr(s)\,ds}S_t
$$
is a martingale. But instead (see [1]) no arbitrage theory dictates that the process
$$
M_t:=e^{-\int_0^tr(s)\,ds}S_t+D_t
$$
is a martingale where $D_t$ is the pathwise present value of all dividends $d_i$ paid until time $t\,$:
$$
D_t=\sum_{t_i\le t} d_i\,e^{-\int_0^{t_i}r(s)\,ds}\,.
$$
To understand this a bit better note that the portfolio consisting of the stock plus its past dividends, when they got put into the money market account, is
$$\tag{1}
\Pi_t=S_t+\sum_{t_i\le t} d_i\,e^{\int_{t_i}^tr(s)\,ds}\,.
$$
This is an asset that does not pay dividends. Hence $e^{-\int_0^tr(s)\,ds}\Pi_t$ must be a martingale, and it obviously equals $M_t\,.$
A natural assumption is that the stock $S_t$ jumps down by $d_i$ at the dividend payment date $t_i\,:$
$$
S_{t_i}-S_{t_i-}=-d_i\,.
$$
Since the second term in (1) jumps up by $d_i$ at $t_i$ it follows that $\Pi_t$ is a continuous process. It is sometimes called cum dividend process of $S_t\,.$ A simple model you can assume is that $\Pi_t$ now follows a GBM with a certain constant vol $\sigma_{cum}\,:$
$$\tag{2}
\Pi_t=\Pi_0\exp(\textstyle\int_0^tr(s)\,ds +\sigma_{cum}W_t-\frac{\sigma^2_{cum}t}{2})\,.
$$
Ignoring dividends that have been paid before $t=0$ yields $\Pi_0=S_0\,.$
To calculate the forward price of the stock we can use the martingale property:
$$
E[e^{-\int_0^tr(s)\,ds}\Pi_t]=\Pi_0=S_0\,.
$$
This gives
$$
E[e^{-\int_0^tr(s)\,ds}S_t]+\sum_{t_i\le t} d_i\,P(0,t_i)=S_0
$$
where $P(0,t_i)=E[e^{-\int_0^{t_i}r(s)\,ds}]$ are discount factors. This yields the formula for the forward price of the stock:
$$\tag{3}
\boxed{F_t=\frac{E[e^{-\int_0^tr(s)\,ds}S_t]}{P(0,t)}=\frac{S_0-\sum_{t_i\le t} d_i\,P(0,t_i)}{P(0,t)}\,.}
$$
If you compare this with the traditional
$$
F_t=S_0e^{(r-q)t}
$$
you can get the levels of $d_i$ from your continuous dividend yield $q=5\%\,.$ For a single $d_i$ or for $d_1=...=d_n$ (this is what you seem to assume) this is very easy. Clearly the level of $d_i$ depends on how many dividends you assume to be known in advance.
BTW: The model assumption (2) was not used to derive (3). Only the martingale property of $M_t=e^{-\int_0^tr(s)\,ds}\Pi_t\,.$ In other words: (3) holds for every arbitrage free model of the stock that only assumes a couple of dividends $d_i$ are known in advance.
[1] D. Duffie, Dynamic Asset Pricing Theory. Princeton University Press, 1991.
