We break 432 into primes:

432 = 2*2*2*2*2*3*3*3

To make the sum as large as possible, we have to get as many of 
the 5 rolls to be 6's as possible.

The most number of 6's we can make by grouping the factors of 432 is 3,
like this

(2*3)(2*3)(2*3)*2

And to make 5 factors we have to use a 1 factor:

432 = 6*6*6*2*1 and 6+6+6+2+1 = 21 is the largest possible sum.

Edwin