5. The sum of all two-digit numbers that are multiples of both 6 and 8 is
【Analysis】A number that is both a multiple of 6 and 8, first factorize the prime factors, 6 is $2 \times 3$, 8 is $2 \times 2 \times 2$, then find the least common multiple,

The two-digit common multiples are only four numbers: $24, 48, 72, 96$, adding them up gives the answer 240.
【Solution】Solution: According to the analysis, first factorize the prime factors $6=2 \times 3, 8=2 \times 2 \times 2$, then the least common multiple of the two is 24,

All two-digit common multiples that meet the conditions are: $24, 48, 72, 96$;
The sum of all these two-digit numbers: $24+48+72+96=240$,
Therefore, the answer is: 240.