$5 、 From 0$ to 9, take any 3 numbers to form a three-digit number without repetition, the probability that this number is not divisible by 3 is $\qquad$ .
5. $\frac{35}{54}$

Analysis: Divide the ten digits into three sets: $A=\{0,3,6,9\} ; B=\{1,4,7\} ; C=\{2,5,8\}$ . Then all three-digit numbers divisible by 3 must either belong to the same set or belong to different sets, totaling: $C_{3}^{1} A_{3}^{2}+2 \times A_{3}^{3}+3^{3} \times A_{3}^{3}+3^{2} \times C_{2}^{1} A_{2}^{2}=228$ , and a total of $C_{9}^{1} A_{9}^{2}=648$ three-digit numbers can be formed, hence $P=1-\frac{228}{648}=\frac{35}{54}$