Five cubic dice were rolled

If we assume these are regular dice being rolled one at a time, the answer would be

...unless, of course,

...unless, of course

However:

The regular cubic backgammon dice have a number of dots from 1 to 6. The divisors of 432 are 1,2,3,4,6 the best chance to obtain the maximum sum is if the the combination has the most divisors. If we assume we throw one or two dice at a time we obtain the following combinations and their sum.

6,6,6,2,1 the sum is 21

4,4,3,3,3 the sum is 17

6,6,4,3,1 the sum is 20

6,4,3,3,2 the sum is 18

To obtain the maximum sum 6+6+6+6+6=30 we have the least probability. In addition to that $6^5$ is far greater than 432. So I will bet as maximum sum 20.