What an awesome problem!
Let's manipulate quantity A to look something like this 5^20/5*4 - 5^19/5*4. Notice that the we can cancel one 5 of the numerator, resulting in 5^19/4 -5^18/4. Next step is to multiply quantities A and B by 4, so we can eliminate that horrible division, resulting in quantity A 5^19 - 5^18 and quantity B (4)(5^18).

Now let's add to both quantities 5^18 think of it like an x variable that we have in both quantities. So we are left with:
Quantity A 5^19
Quantity B (5)(5^18). (if we have already 4x and we add one more x, is 5x. where x=5^18)

Now (5)(5^18) can be rewritten as 5^19, thus correct answer is C.