5. On each face of an opaque cube, a natural number is written. If several (one, two, or three) faces of the cube can be seen at the same time, then find the sum of the numbers on these faces. Using this method, the maximum number of different sums that can be obtained is _.

翻译结果如下：

5. On each face of an opaque cube, a natural number is written. If several (one, two, or three) faces of the cube can be seen at the same time, then find the sum of the numbers on these faces. Using this method, the maximum number of different sums that can be obtained is _.
5.26 .

There are 6 cases where a single face can be seen, 12 cases where two faces sharing a common edge can be seen simultaneously, and 8 cases where three faces sharing a common vertex can be seen simultaneously, thus yielding 26 sums. The numbers on the faces can be filled in such a way that all 26 sums are distinct (for example, the numbers $1, 10, 10^{2}, 10^{3}, 10^{4}, 10^{5}$ can be written on the 6 faces).