5. Among the five-digit numbers formed by the 3 digits $1,2,3$, $1,2,3$ each appear at least once. There are $\qquad$ such five-digit numbers.
5.150.

Among the five-digit numbers,
if 1 appears only once, there are $\mathrm{C}_{5}^{1}\left(\mathrm{C}_{4}^{1}+\mathrm{C}_{4}^{2}+\mathrm{C}_{4}^{3}\right)=70$;
if 1 appears twice, there are $C_{5}^{2}\left(C_{3}^{1}+C_{3}^{2}\right)=60$;
if 1 appears three times, there are $\mathrm{C}_{5}^{3} \mathrm{C}_{2}^{1}=20$.
Therefore, there are a total of 150 such five-digit numbers.