The explanation is as follows:
Q1 can't be A because it asks which one has the answer as B. Can't be B because then Q1 is already the one with the first answer as B. If Q1 is D, then Q2 links to Q4 saying that 3 questions have the answer as D, and since we already know the answer to Q2 and Q4 none of which are D, then Q1, Q3, and Q5 are D, but Q3 can't be D because according to Q3 and choosing D, the answer to Q1 is A, but we already know that the answer to Q1 isn't A, so this choice fails as well. Therefore the only option left is C.
For Question 3
We know that the correct answer to Q1 is C, and that says that Q3 is the first question with the answer as B, so therefore Q3 is B.
For Question 4, 2, and 5
If we choose A, then there are only 2 questions left which can have the answer as D, but A says there are 3 left, so therefore A is false. Also, we can cross out D because if it is indeed zero, then the answer for this question can't be D. It can't be B because that means Q2 and Q5 have the answer as B because then Q2 says the answer to Q4 is C, but we have chosen B. Therefore only C works, which means Q2 has the answer D. And then the only answer that works for Q5 is B.