First tell us what the problem really says! "would divide by 498" is bad grammer and meaningless. Do you mean "would divide 498" or "is divisible by 498"?
Second, let the smaller of the numbers be x so that the other is 5x. Their sum is 6x. Now you need either that is an integer or that is an integer depending upon which of the above you meant. In either case, the fact that 498= 6(83) helps. The fact that 83 is prime is also important.