The probability of getting an even number on any one die in a single roll is [tex]\dfrac12[/tex].
For 5 dice, the probability of rolling [tex]x[/tex] even numbers (where [tex]0\le x\le5[/tex]) is
[tex]p(x)=\dbinom5x\left(\dfrac12\right)^x\left(1-\dfrac12\right)^{5-x}[/tex]
[tex]p(x)=\dbinom5x\left(\dfrac12\right)^5[/tex]
You then have
[tex]p(4)=\dbinom54\left(\dfrac12\right)^5=\dfrac{5!}{2^54!(5-4)!}=\dfrac5{2^5}\approx0.156=15.6\%[/tex]
