[tex]\mathbb P(X<6)=\mathbb P(X=0)+\mathbb P(X=1)+\cdots+\mathbb P(X=5)[/tex]
[tex]X[/tex] appears to have a binomial distribution, which means
[tex]\mathbb P(X=x)=\dbinom Nx p^x(1-p)^{N-x}[/tex]
where [tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]. So, as an example, you could compute
[tex]\mathbb P(X=0)=\dbinom{20}00.3^0\times0.7^{20}=0.7^{20}\approx0.0007979[/tex]
You should get
[tex]\mathbb P(X<6)=\displaystyle\sum_{x=0}^5\mathbb P(X=x)\approx0.4162[/tex]
