5. A certain middle school offers six elective courses: $A, B$, and $C$ are the first category of elective courses, and $D, E, F$ are the second category of elective courses. It is required that each student selects three courses, with at least two courses from the first category. Now, there are three students, Jia, Yi, and Bing, selecting courses. The probability that any one student has at least two elective courses in common with the other two students is $\qquad$
5. $\frac{79}{250}$.

The number of different choices for each student is
$$
\mathrm{C}_{3}^{2} \mathrm{C}_{3}^{1}+\mathrm{C}_{3}^{3}=10 \text {. }
$$

If all three students choose the three subjects $A, B, C$, there is 1 way; if exactly two of the three students choose the three subjects $A, B, C$, there are $\mathrm{C}_{3}^{2} \mathrm{C}_{3}^{2} \mathrm{C}_{3}^{1}=27$ ways;

If exactly one of the three students chooses the three subjects $A, B, C$, there are $\mathrm{C}_{3}^{1}\left(\mathrm{C}_{3}^{2} \mathrm{C}_{3}^{1} \mathrm{C}_{3}^{1}+\mathrm{A}_{3}^{2} \mathrm{C}_{3}^{1}\right)=135$ ways;

If none of the three students choose the three subjects $A, B, C$, there are $C_{3}^{1} C_{3}^{1} C_{3}^{1} C_{3}^{1}+C_{3}^{2} C_{3}^{1} C_{2}^{1} C_{3}^{1}+A_{3}^{3} C_{3}^{1}=153$ ways.
Therefore, there are a total of $1+27+135+153=316$ ways.
Thus, the required probability is $\frac{316}{10^{3}}=\frac{79}{250}$.