The fact that none of the rearrangements are even means that each individual roll is odd.

The fact that we are told that b>d and we are expected to figure out the entire sequence must mean that there are four rolls of one number and one roll of a second number.

The gives few enough possibilities for trial and error. We need to try each of five rearrangements of 13333, 15555, 31111, 35555, 51111, 53333 for divisibility by 7.

The only one that is never divisible by 7 is 35555, therefore the sequence of dice rolls was 55535.

For completeness, the sequences that are never divisible by 7 are:

11111 and its multiples 22222 33333 44444 55555 66666

11112 and its multiples 22224 33336

The result of subtracting those three from 77777: 66665 55553 44441

Every other sequence of dice rolls can be arranged to be a multiple of 7.