what is the probability to get a sum $s$ after $n$ independent random number generation events. We have the probability $P(X=x)$, i.e. the probability that the random number $X$ gets the value $x$. Let's assume that $x \in [0,x_{max}]$. Formally:
$$\sum_{t=1}^{n}X(t) = s~, \quad \text{with}~~ s > x_{max} ~~ \text{in general.}$$
The problem can be viewed as 'n' unfair dice rolls $x \in [0,5]$ with sum $s$.
Thank you.