Supposedly, all the logic that follows the basic adder will conditionally adjust the output for base 5.
With decimal adjust circuits, one adds 6 to the sum digit when it is greater than 9, but add nothing if the sum is not. That will adjust the sum digit, and force a carry out for sums > 9.
Work it out in hex or binary to see that the above method works.
The base 5 circuit ought to be doing a similar thing, but with a different adjustment value.