5. A bag contains five white balls, four red balls, and three yellow balls. If four balls are drawn at random, the probability that balls of all colors are included is $\qquad$ .
5. $\frac{6}{11}$.

The balls drawn have three possibilities: two white, one red, and one yellow; one white, two red, and one yellow; one white, one red, and two yellow. Therefore, the required probability is
$$
p=\frac{\mathrm{C}_{5}^{2} \mathrm{C}_{4}^{1} \mathrm{C}_{3}^{1}+\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{2} \mathrm{C}_{3}^{1}+\mathrm{C}_{5}^{1} \mathrm{C}_{4}^{1} \mathrm{C}_{3}^{2}}{\mathrm{C}_{12}^{4}}=\frac{6}{11} .
$$